







An arch in the form of a semiellipse 
20200420 

From Anggelica: an arch in the form of a semiellipse is 8 feet wide at the base and has a height of 4ft. how wide is the arch 1foot above the base? Answered by Penny Nom. 





A parabolic arch 
20200206 

From icyy: how high is the parabolic arch of span 20 feet and height of 16 feet, at a distance 5 feet from the center?
what equation will I be going to use? thank you Answered by Penny Nom. 





The length of an arc 
20190428 

From Patrick: If an arch is 48 inches wide at the base and 30 inches tall at its apex, what is the length of the arch? Answered by Penny Nom. 





Distance between a chord and its arc on a circle 
20180323 

From Doug: Specifically, what is the subject distance for the Earth orbiting for 27 days. Assume the orbit of the Earth to be a circle have a 93 million mile radius. Assume the angle of arc to be (27/365) x 360 degrees. Thank you. Answered by Penny Nom. 





An arched window 
20170724 

From Gerry: Looking to make a full size template for an arched window. Need increments every 16". The radius is 138' 0 9/16" , the chord is 226" and the rise at center of chord is 43" Answered by Penny Nom. 





A parabolic arch 
20170105 

From Rand: It is most likely already been answered but I can not seem to find the right key words for the search engine?.
What I am looking for is, if you have an have arch/arc and you know the degree of slope and the height of the arch/arc from ground lvl; how do you factor the decreasing angle/#’s to get the distance tween the two feet on the assumption that the arch/arc is curved all the way to ground lvl?
a. where the legs widen continuously (till they hit ground) so yes parabolic &
b. where the legs come down straight after a ½ circumference run.
What I am focusing is the parabolic.
Many Thanks Answered by Harley Weston. 





Radius angle and arc length 
20161124 

From pavidthra: Length or arc 11 and angle of subtended 45.need to find a radius Answered by Penny Nom. 





A search area 
20160813 

From tammy: if your searching an area and you go 300 km from point A and search 380° what or how much area would you search? Answered by Penny Nom. 





A sector of a circle 
20160421 

From mustafa: In a sector of a circle, the arc length is equal to half the perimeter of a sector.find the area of a sector in terms of r Answered by Penny Nom. 





Heights at various points along an arc 
20160415 

From Isiah: So I am working on a problem with a few friends; you have an arc with the center of its chord at 0,0. We also have a known sagitta and a known radius of curvature.
How do we calculate the height extending in both the positive and negative directions?
Central sag: 2.48
Chord length: 9.6 Answered by Penny Nom. 





tan inverse 1/4 
20160314 

From nazz: prove; tan inverse 1/4=1/3 cot inverse 52/47 Answered by Chris Fisher. 





Shooting a ball at a target 
20160216 

From Thys: Hi
I have a problem with the formula that i use .(for programming)
I have looked all over the web to find a solution but no luck.
I have a cannon that shoots a ball at a target
I use this formula to calculate what my initial velocity must be to hit the target
at a angle of 30 degrees and a distance of 15m (the cannon and target position is known)
It works perfectly if both is at same height but if one is higher or lower it miss.
In an example I am working with the range is 30m, the angle is 45 degrees and the target is 10m higher than my position.
Please help
Formula = V0 = √RG / Sin(2α) Answered by Harley Weston. 





A chord of a circle, the central angle and the radius 
20160126 

From Nishan: If chord length is given along with angle then how to calculate the radius. Answered by Penny Nom. 





The height of a parabolic arc 
20151230 

From Tom: Is there an algebraic means to determine the highest point of a parabolic arc if the base and perimeter are known? Answered by Penny Nom. 





Drawing an arc 
20151204 

From hassan: how to draw a curve long 1m with an angle of 22.5? Answered by Penny Nom. 





A parabolic arch 
20151130 

From Muhammad: An arch over a road has a parabolic shape it is 6 meter wide at the base and is just
tall enough to allow a truck 5 meter high and 4 meter wide to pass
a):
assuming that the arch has an equation of the form y=a(x)^2+b use the given
information to find a & b. explain why this assumption is reasonable.
b):
sketch the graph of arch equation Answered by Penny Nom. 





Archimedes, Euclid and "Circular Reasoning" 
20151115 

From Ron: I have read about Archimedes and his work with sphere in cylinder and cone in cylinder and the volume relationships. Did he or any others also extend this to regular based polygon based regular like pillars, and columns? The ratio of 1/3 to 1 whole holds true with all regular based columns as example: a regular pyramid having a regular hexagon base inside a regular hexagon column of equal height. Answered by Chris Fisher. 





The distance over a Quonset 
20150820 

From jane: total base of hemisphere is 30 ft
apex height is 20 feet
what is total length over dome Answered by Penny Nom. 





Locating the center of a circle that forms an arc 
20150423 

From Ken:
Find the Cartesian coordinates of the center of an arc with the given location of the beginning and end points and radius length. Not the midpoint of the circumference but the actual point that the arc
is drawn around.
I know their are two answers depending on the direction of the arc. Unless we assume that all arcs are drawn counter clock wise.
Thanks
Ken
Answered by Harley Weston. 





The perimeter of a parcel of land 
20140918 

From Shirley: What is the perimeter of a parcel of land that is 564 acres square Answered by Penny Nom. 





A chord and an arc of a circle 
20140806 

From Luis: Hello I am trying to figure out how to get chord lengths of quarter points for a circle. I work with large diameter circles and I need to be able to find chord length from 0 degrees to 90 degrees, 0 degrees to 270 degrees, 270 degrees to 180 degrees and 90 degrees to 180 degrees. Can you please use 100ft. diameter as example and work out the problem. I'm sorry if I use wrong terminology, I'm really bad at math . Thank you in advance for your time and help I really appreciate it. Answered by Harley Weston. 





An arc subtended at the center of the Earth 
20140720 

From Abhinav: Meerut is 60 km from Delhi. Find the nearest second the angle subtended at the center of the earth by the arc joining these two points,earth being regarded as a sphere of 5940 km radius. Answered by Penny Nom. 





A reversed curved on a railroad track 
20140619 

From cherrielyn: Assuming that earth is a sphere of radius 6380 km,
what is the difference in the latitudes of two cities 270 miles apart
positioned on the same meridian?
Thank you in advanced po! :) Answered by Penny Nom. 





Two overlapping arcs in a square 
20140315 

From Jean: I have a square with side 4 cm. There are two overlapping arcs going from vertex to diagonal vertex. The other two vertices are the center of the arcs, which are shaded. How do I find the area of the shaded arcs? The overlapping arcs when shaded resemble a long thin football
Thank you for your help. Answered by Penny Nom and Walter Whiteley. 





A chord length of 2 cm 
20140313 

From prema: I am having only chord length as 2cm. how to find arc length and degree Answered by Penny Nom. 





A circle, a chord and an arc 
20130416 

From Tim: Morning,
I was told the chord is 3000mm and the depth of chord is 300mm, I can
find the radius,(1500 squared + 300 Squared) Divided by (300 + 300)
but don't know how to calculate the length of the circle defined by the chord.
Regards
Tim
Answered by Penny Nom. 





The degree measure of the central arc of a circle 
20121017 

From Crystal: On a circle with radius of 12 cm is an arc of length 20 cm. What is the degree measure of the central angle used to make this arc? Answered by Penny Nom. 





A tapestry rod on a curved wall 
20120814 

From Marlyn: I have a curved wall with a radius of 6'. I am trying to have a 36" rod made to hang a tapestry and need to figure out the degree measure of the arc.
Can you help me please? Answered by Penny Nom. 





Archimedes Burning Mirror 
20120717 

From Frakeetta: Archimedes Burning Mirror
There is a story about Archimedes that he used a “burning mirror” in the shape of a paraboloid of revolution to set fire to enemy ships in the harbor. What would be the equation of the parabola that one would rotate to form the appropriate paraboloid if it were to be designed to set fire to a ship 100m from the mirror? How large would the burning mirror need to be? What is the likelihood that this story is true? Answered by Robert Dawson. 





A parabolic arch 
20120104 

From Swathi: A plan for an arch in the shape of a parabola is drawn on a grid with a scale of 1m per square.
The base of the arch is located at the points (0,0) and (15,0). The maximum height of the arch
is 18m.
a)Determine the quadratic function that models that arch
b)State the domain and range of the function Answered by Penny Nom. 





How much work is done? 
20111015 

From Jean: "A conical buoy that weighs B pounds floats upright in water with its
vertex "a" feet below the surface. A crane on a dock lifts the buoy
until its vertex just clears the surface. How much work is done ?" Answered by Penny Nom. 





The length of an arc 
20110824 

From nuel: Is there any formula to calculate the arc length from only the chord length and angle between the chord and tangent of the arc at its endpoint ? Answered by Penny Nom. 





Find the rate at which the searchlight rotates 
20110417 

From Meredith: A searchlight is position 10 meters from a sidewalk. A person is walking along the sidewalk at a constant speed of 2 meters per second. The searchlight rotates so that it shines on the person. Find the rate at which the searchlight rotates when the person is 25 meters from the searchlight. Answered by Penny Nom. 





The degree measure of an arc in a circle 
20110408 

From Deb: How do I find the degree measure of an arc in a circle with the Length of 14 and the radius of 70? Answered by Penny Nom. 





A region bounded by a chord and an arc 
20110228 

From Gene: find the area of a segment bounded by a chord and a 45 degree arc of a 36" circle Answered by Robert Dawson. 





A sector of a circle 
20110107 

From Alice: the radius of a circle is 7cm the angle of the sector is 68 how do you find the Answered by Penny Nom. 





Will the ball clear the tree? 
20101114 

From MK: Sam hits a golf ball with a fiveiron a distance of 120m horizontally. A tree 45m high and 35m in front of Sam is directly in the path of the ball. Will the ball clear the tree if the ball makes a parabolic curve and has a maximum height or 80m? Answered by Brennan Yaremko. 





The low leg height of a shutter 
20100520 

From brian: I work for a shutter company and am in need of a formula to figure
out what the low leg height would be if given the width of shutter,
the high point of arch top and the radius. example would be a 18" wide
shutter with a 80" high leg on the right side and a 30" radius. I would
need a way to figure what the low leg height (left side of shutter)
would be. Or if given width, low leg height and radius what the high
side would be? If any of this can be given in laymen's terms it would be
much appreciated.
Thanks,
Brian Answered by Harley Weston. 





Body measurements 
20100406 

From Amirul: Recently I'm proposing my research question to my teacher for my extended essay. I'm an IB student.
My research question is regarding the estimation of human in buying trousers through reference of neck. What does the relation between the diameter of the neck and the diameter of the waist?
I want to see how far does the estimation theory is true for different type of people with different BMI(body mass index)..
But teacher said that it is golden ratio...so nothing interesting... =(
really??? But i search on net.... state that my idea seems do not have any relation with the golden ratio so far..... i just want ask you... am I able to perform in my extended essay if i continue with this research question?? Answered by Robert Dawson. 





Arc length and Chord length 
20100313 

From Darryl: Is there a formula to determine the chord length of an arc knowing only the arc length and the arc depth (sagitta)? I know you can't find the radius with only these two inputs, but can you find the chord length? Answered by Harley Weston. 





The distance from a chord to an arc 
20100211 

From matt: hello, I have to layout a radius without being able to pull from the center my radius is 3819.53 feet and i have a chord length of 275.59 feet if i broke that up into 25.05 feet sections how would i calculate the lengths from my chord to that radius? Answered by Robert Dawson. 





A tunnel from Toronto to Montreal 
20100125 

From Dave: I want to make a tunnel from Toronto to Montreal (for example)
Something like this
http://mathcentral.uregina.ca/QQ/database/QQ.09.09/h/grant1.html

My coordinates are 45.442455,73.861340 (Montreal) and 43.442455, 79.861340 (Toronto)
I need to know how to find arc distance, chord distance and radius
What websites can i find for this subject
Google has many but they are useless (blah blah) websites
LOL
Thanks Answered by Chris Fisher and Robert Dawson. 





The height of an arch 
20100102 

From kamer: given the radius 1.696 also the cord length 1.958 find the height between the cord and the arch. Answered by Penny Nom. 





Chord length given the length & radius of an arc 
20091231 

From Wayne: Given the length & radius of an arc, is there a formula that will accurately calculate the chord length?
I'm an architectural designer, and would need it explained in layman's terms. Thank you.
Wayne Answered by Penny Nom. 





The radius of an arc 
20091013 

From AYMAN: Question from ayman:
i would like to know the radius of an arc , i do not know the angle , can u please explian it with an example ,
all i know , or i think i know is a draw line , the reason i asked yu guys this Q , is i am a boilermaker apprentice , sometimes i do deal with a bended pipes or flate plates of metal .
when i try to do the same bend as these pipes , it is quite hard so for me to find out the radius of the pipe already bended & find out the angle i will be able to know the full length of the material thats all , thank you Answered by Robert Dawson. 





Sagitta 
20090910 

From Robert: Can you please tell me if there is a formula to figure out the Sagitta of an
arc when you know the radius, chord length, and arc length? Answered by Chris Fisher and Harley Weston. 





Find the central angle 
20090818 

From Larissa: In a circle, the length of a chord AB is 4 cm and the length of the arc AB is 5 cm. Find the central angle theta, in radians, correct to four decimal places. Then give the answer to the nearest degree. I think I'm supposed to use Newton's method, but am not sure how to start with this problem. Answered by Harley Weston. 





The layout of an arch 
20090818 

From Steven: I am trying to layout a large radius between 2 points in a building and
need a formula to figure different senarios for example:
radius is 187'6"
distance between 2 points is 34'8"
need points 16" apart along the line between the 2 points to create the
radius
please help Answered by Stephen La Rocque. 





Arc length 
20090710 

From farhad: hi
i need to measure length of arc by having only two measurements, first the length of the chord and
the height of the curve.
if i have a simple calculator that haven't sin cos tang (i want to calculate it in my mind) Answered by Stephen La Rocque. 





The radius of an arc 
20090612 

From Billy: I have tried using the formula 4h2(squared)plus L2(squared)divided by 8h
to find the radius of an arc, but I must be doing something wrong since I keep
getting the wrong answer. Can you tell me what I am doing wrong. The height
is 37.75 in. and the length is 18.875 in. Thank you for any help you can
give me. Answered by Stephen La Rocque. 





An arched or round top window 
20090407 

From Dale: I need a formula to figure the lineal footage of trim require to trim an arched or round top window. The variables that I have consist of the width of the window the height of the arc and the radius. Answered by Harley Weston. 





The length of an arc 
20090404 

From Dale: If I have the length of the chord and the height of the arc can I find the arc length with these dimensions? Answered by Harley Weston. 





The height of an arc at the peak 
20090401 

From Ed: What is the term used to describe the height of an arc at the peak? Answered by Stephen La Rocque. 





A parabolic arch 
20090328 

From Jeni: A doorway is in the shape of a parabolic arch.
Find the width of the doorway 1m above the floor.
Given: the height and the width of the doorway is 4m and 3m respectively. Answered by Penny Nom. 





A cord length and angle measurement 
20090326 

From larry: i have a radius of 185". and an arc length of 186.5". how do i find the arc degrees
or cord length? Answered by Harley Weston. 





Forming an arc with 2 inch steel 
20090211 

From Craige: I need to calculate the bending radius of 2" wide steel to achieve given inside and outside arc lengths Answered by Harley Weston. 





Archimedes' formula for parabolic arches 
20090123 

From La: Use calculus to verify Archimedes' formula for y=9x^2. Prove Archimedes' formula for a general parabolic arch. Answered by Harley Weston. 





Parallel distances from arc of circle to its chord 
20090116 

From Roger: Give the length of a chord of a circle and the height of the arc, how do I
find the lengths of equally spaced parallel lines drawn from the chord to
the arc. (Think of the lengths of vertical slats in an archtopped bed head
board.) Answered by Chris Fisher and Stephen La Rocque. 





An arch is in the form of a semi ellipse 
20081103 

From jessica: An arch in the form of a semi ellipse has a span of 10 meters and a
central height of 4 m. Find the heights of the arch at a point of 3 meters from the semi minor axis. Answered by Penny Nom. 





A bay window 
20081030 

From Scott: Given the length of an arc, the rise of an arc, and the number of segments
that I need to divide the arc into  how do I determine the length of each
segment? Imagine a bay window. It could have 5 side or 7 sides, just as
an example. How do I determine the width of each window given that the
unit will be mounted into a frame with a 96 inch opening. The rise of the
unit will extend out 18 inches. Lets say that the number of single windows
unit within the unit is 5. How wide should each window be? Do you
understand? Answered by Harley Weston. 





An arc and an angle 
20081005 

From Cory: I have a chord length of 150'. From the left starting point, I know that
30' right of starting point is 9' in height. This would be the top of the arc.
What is the arc in degrees and can anyone display an image to help me
understand? Answered by Penny Nom. 





Finding the Distance Between Two Latitudes 
20081002 

From Samua: Assuming that the Earth is a sphere of radius 4000 miles and that the cities
are on the same longitude (one city is due north to the other). Find the distance between
the cities with the latitudes of 37 degrees 47'36'' and another city with 47 degrees 37'18''. Heeeeeeeeeeelp! Answered by Janice Cotcher. 





The length of an arc 
20080904 

From Angie: Segment PR is a diameter of circle S. If angle P =3D 25, find minor
arc QR.
This circle has an isosceles triangle in it, it is connected to the
diameter, Answered by Harley Weston. 





Arclength and sectorangle 
20080806 

From Benson: If chord length, radius are given, How to find the sector angle and arclength Answered by Janice Cotcher. 





The length of an arc 
20080714 

From Chris: trying to find the length of an arc or segment of a circle when
the radius or circumference is unknown
take a circle, put a line across the circle label it A /B /C
A and C are the end points, B is the middle
line length is 86. From B to the side of circle is 16. Label that point D
need to find the length of A D C Answered by Penny Nom. 





Chords and arcs 
20080711 

From Ronnie: We are trying to build a semi life size ark decoration , and we are trying to cut the sides out . The curved sides and we can't figure our radius , all we know is that our chord length is 24ft. any suggestions on how to find the radius or maybe even the arc length or circumference or diameter? Answered by Harley Weston. 





A fivesided coin 
20080629 

From carla: A new fivesided coin is to be made in the shape of figure 8.6
The point A on the circumference of the coin is the centre of arc CD, which has a radius of 2cm
Similarly B is the centre of arc DE, and so on.
Find the area of one face of the coin. Answered by Harley Weston. 





A space camera circles the Earth 
20080616 

From Rita: A space camera circles the Earth at a height of h miles above the surface. Suppose that d distance, IN MILES, on the surface of the Earth can be seen from the camera.
(a) Find an equation that relates the central angle theta to the height h.
(b) Find an equation that relates the observable distance d and theta.
(c) Find an equation that relates d and h.
(d) If d is to be 3500 miles, how high must the camera orbit above Earth?
(e) If the camera orbits at a height of 400 miles, what distance d on the surface can be seen? Answered by Penny Nom. 





If the arc is 75mm, what is the radius? 
20080612 

From malcolm: If the are is 75mm, what is the radius? Answered by Janice Cotcher and Harley Weston. 





Arclength 
20080607 

From prem: i am engineer, i need the formula for calculate the arclength by using only chord length and radius only Answered by Penny Nom. 





A bridge is built in the shape of a parabolic arch 
20080602 

From megan: A bridge is built in the shape of a parbolic arch. The bridge has a span of 192 feet and a maximum height of 30 feet. Find the height of the arch at 20 feet from its center. I need the equation and what to fill into the equation...please and thankyou! Answered by Penny Nom. 





The length of an arc 
20080516 

From Don: I am trying to determine the length of an arch with a two foot backset from 32 foot frontage. Answered by Harley Weston. 





The length of an arc 
20080512 

From patricia: Find the length of the arc on a circle of radius r = 16 inches intercepted by a central angle [theta] = 60 degrees Answered by Penny Nom. 





Chord, radius, arc length and central angle 
20080415 

From Cindy: There is a railroad curve with a chord length of 2000 ft. and a central angle of 35 degrees. What is the radius and arc length of the circular arc? Answered by Stephen La Rocque. 





A parabolic arch 
20080214 

From Angela: A parabolic arch has an equation of x^2 + 20y  400 = 0 where x is measured in feet. How do I find the maximum height of the arch? Answered by Penny Nom. 





The radius of a circular arc 
20080204 

From Bill: Hi,the Central Angle of a sector of a circle is 40 degrees. The circular arc of the curve has a chord length of 3000 ft. Find the radius(r) of the circular arc. Answered by Penny Nom. 





A large concrete shape 
20080116 

From Keith: what is the cubic yards of an area that is not a perfect 1/4 circle?
The dimensions are 100ft. x 60ft. x 125ft. curcumferal arch x 3ft. depth? Answered by Stephen La Rocque. 





Lining up coins visually using geometry and trigonometry 
20071231 

From Jessica: a) In what order would you arrange a penny, a nickel, a dime, a quarter, and a halfdollar so that they all have the same apparent size? The diameters of the coins, in thousandths of inches, are as follows: penny, 750; nickel, 835; dime, 705; quarter, 955; halfdollar, 1205.
b) How should the coins be placed, if the distance between the dime and the halfdollar is 100 units?
How far from thw dime should your eye be to see that all the coins have the same apparent size?
c) What angle do the coins subtend when they have the same apparent size? Answered by Stephen La Rocque. 





How would one find the radius? 
20071229 

From Ned: Given an arc with length of 192 inches (don't know chord length),
and arc height of 6 inches, how would one find the radius? Answered by Stephen La Rocque and Harley Weston. 





An arched entry 
20071128 

From amber: i am working with an arched entry. i know that the radius is 25' and the height is 20'11". i need to know the length of the arch and degree of bend of the arch. how do i find these? Answered by Stephen La Rocque. 





The radius of an arch 
20071110 

From Mark: How do you determine the raduis or diameter of a circle based on the folowing information:
1. The distance along the circle between two points is 35'2". This creates an arch.
2. The (chord) distance between the two points is 30'8".
3. The distance from the center of the chord (on a 90 degree) to the arch is 6'10 3/4". Answered by Harley Weston. 





Completing the square 
20071101 

From Mark: An architect is designing a museum entranceway in the shape of a parabolic arch represented by the equation y = x2 + 20x, where 0 x 20 and all dimensions are expressed in feet. Determine the maximum height, in feet, of the arch. Answered by Stephen La Rocque. 





parabolic arch 
20071024 

From ABHILASH: How find parabolic arch perimeter. Answered by Harley Weston. 





Arc length and height in a circle 
20071023 

From Bruce: I have been trying to find a formula that relates height of a segment
from the bottommost point of a circle toward the center of the circle to
the corresponding distance along the circumference of the circle
(i.e. at the point on the circumference intersected by a line perpendicular
to that segment). The unknown variable is the height of the segment;
the known variables are the radius of the circle and the distance
along the circumference. Answered by Stephen La Rocque. 





Given the arc length and chord length, what is the radius? 
20071010 

From Wayne: I have the actual length of an arc plus the length of the cord. How do I determine the radius of the arc. Answered by Harley Weston. 





Parabolic arch 
20071009 

From Nisa: A parabolic arch has a span of 120 feet and a maximum height of 25 feet. Choose suitable rectangular coordinate axes and find the equation of the parabola.
Then calculate the height of the arch at points 10 feet,20feet,and 40 feet from the center. Answered by Stephen La Rocque. 





Arc lengths, central angles and radii 
20071004 

From Ashutosh: Jose can remember that the length of an arc is 440cm, but he cannot remember the radius of the arc or the angle at the center. He does know that the angle was a whole number of degrees and the radius was less than 100cm. Find three possible angles and write down the size of each of the possible radii. Answered by Stephen La Rocque. 





The length of an arc 
20070926 

From swarna: a wire of length 32 cm is bend to form a sector of circle of radius of 6 cm find the length of the arc of the sector Answered by Penny Nom. 





The perimeter of a regular polygon 
20070918 

From Ashwynn: why does the area of regular polygons with a perimeter of 1000m increase as the number of sides increase? Answered by Stephen La Rocque. 





The height of an arc at the center 
20070717 

From Bob: I have a circle with a 26" radius and a cord whose length is 20". How can I find the height of the arc at the center point of the cord? Answered by Penny Nom. 





The length of an arc 
20070618 

From Lenny: How do you find out the arc length of a sector 50 degrees wide?? Answered by Stephen La Rocque and Penny Nom. 





Babylonian geometry 
20070617 

From marleen: The following problem and the solution were found on a Babylonian tablet dating from about 2600BC:
Problem:60 is the Circumference, 2 is the perpendicular, find the chord.
Solution:
Thou double 2 and get 4
Take 4 from 20, thou gettest 16
Square 16, thou gettest 256
Take 256 from 400, thou gettest 144
Whence the square root of 144, 12 is the chord.
Such is the procedure. Modern day mathematicians have reasoned that the Babylonian Mathematician who solved this problem assumed that the value of Pi is 3. By explaining in detail how the Babylonian Mathematician must have solved this problem, justify the reasoning of the modern mathematicians. Answered by Stephen La Rocque. 





A steel arc 
20070531 

From Huw: Two gate posts 48cm apart and a perfect arc of steel is to be made joining the two posts on top. this steel arc is to measure 12cm higher than the top of the gate posts in its centre point.
the question similar to this was asked by "daryl" and answered by "Penny"
If you could reply to this i would be very grateful. Answered by Penny Nom. 





The circumference of part of a circle 
20070506 

From Wallis: I have more then a quater of a circle, but less than half. What is the circumference if the two side are 7cm and the angle between them is 110 degrees? Answered by Penny Nom. 





An arc shaped groove into a peice of metal 
20070412 

From daniel: hello i work at an engineering workshop the other night i was asked to machine an arc shaped groove into a piece of metal the cord length was 6 mm and the height from the middle of the cord to the arc was 1mm i was hoping to find the diameter of the cutter needed to do the job and also the formula to work out how to find the diameter. i believe it is 10mm dia thankyou for your time and knowledge Answered by Stephen La Rocque. 





A cabinet with an arched front 
20070409 

From Joe: I am building an arched front cabinet that is 71 inches wide, 12 inches deep at both ends
and 16 inches deep at the center. To accurately build this cabinet I need to known the radius of
the circle that would form that arch.
Thanks,
Joe Answered by Penny Nom. 





An arched opening for a large doorway 
20070408 

From Richard: I am trying to build an arched opening for a large doorway...I know the vertical sides of the opening to be 8'9" from the floor to the lowest point of the arch on each side...I know it is 15 1/2" from the center horizontal point to the top of the arc...I know the vertical sides are 11'11" apart...what I need to know is the radius to create the proper arc. Can you help? Answered by Stephen La Rocque. 





A parabolic arch 
20070329 

From A student: I am trying to figure out how to work this problem as it doesn't have many
details.
The problem ask for an equation to satisfy a parabolic arch y = 16  0.25x^2
for y>=0.
Find the width w of the arch. Answered by Stephen La Rocque. 





The width of an arch 
20070328 

From Brad: A parabolic arch satisfies the equation y= 16  0.25x^2 for y >= 0. Find the width w of the arch. Answered by Penny Nom. 





A roadway over a river 
20070312 

From Taranjeet: My teacher has given us bridge with only one measurement. From the river to the roadway is 50 metres in length (vertically) The question he wants us to find out is. What is the distance between the vertical supports. He has said that: At a horizontal distance of 'x' metres from the foot of the arch the height of the arch, the height of the arch above the river 'h' metres is given by: h=1/40(x squared) = 3x I don't understand how to find the distance between the support beams. Thank you Answered by Penny Nom. 





Chords and arc lengths 
20070308 

From Angela: my dad, who is a welder, asked me a question pertaining to chords and points on an arc to which I cannot for the life of me find an answer or an equation. if you could help, it would be much appreciated. I am sending an attachment of the problem. Answered by Stephen La Rocque. 





Find the length of the belt 
20070308 

From Helen: Find the length of the belt Answered by Penny Nom. 





An arc, a cord and the radius of a circle 
20070114 

From Kevin: I have the length of the cord and the distance from the cord to the arc, is it possible to find the radius with just these parameters? Answered by Penny Nom. 





Can the trailer safely pass under the bridge? 
20070102 

From Jim: A truck hauling a doublewide trailer needs to pass under a parabolicarched bridge en route or take a 50 mile detour. The trailer is 14 feet high and 15 feet wide. The arch supporting the bridge at this underpass is 18 feet high at the center and 40 feet wide at the base. Can the trailer safely pass under the bridge? Answered by Stephen La Rocque. 





Splitting A Circle Evenly 
20061220 

From Joe: I'm trying to make a game board and instead of having it square, I would like to give it a curve (the game is Parcheesi). The attached diagram is pretty much completed (done in AutoCAD). What I would like to know is how to manually find the points that intersect the red line. In other words, evenly split the semicircle into 8 pieces. Answered by Penny Nom. 





What is the height of the arc of the earth over a certain distance? 
20061201 

From Thomas: what is the height of the arc of the earth over a certain distance? Answered by Penny Nom. 





The radius of an arch 
20061115 

From Kelly: I am trying to achieve an arc height of .375 on the length of 17.375. Answered by Penny Nom. 





How do I draw the arc? 
20060722 

From Dani: How do I draw the arc (calculate the included angle) when I know only the arc length? Answered by Stephen La Rocque. 





A problem with arc sine 
20060707 

From Scott: How to prove arc sin x = arc tan( (x)/√(1x2))
Answered by Penny Nom. 





Marking out a circle 
20060628 

From Peter: given a straight line. how do i work out the off sets ( at right angles) at several intermediate points. to set out a 5.0m arc that has a 18.0m radius. Answered by Stephen La Rocque and Penny Nom. 





The interior angles of a right triangle 
20060520 

From Greg: I am wondering if there is a way to figure out the interior angles of a right triangle if we know ONLY the side lengths, and the trick is, we CANNOT use arctangent! Answered by Leeanne Boehm and Penny Nom. 





A fountain of water jets forms parabolic arches 
20060503 

From Jennifer: Let's say in you have a fountain and the water jets form parabolic arches. The center of the fountain, being the origin of the coordinate system, it is elevated 5 feet off the ground, . The equation formed the water arch is y= x^{2}+4x, what is the radius of the basin needed to catch the water at ground level? Answered by Stephen La Rocque. 





A parabolic arch 
20060502 

From Mike: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the center of the arch? Answered by Stephen La Rocque. 





The diameter of a pipe 
20060127 

From An other:
I know the base length of my arc (10 inches)  I also know the height at the center to the arc (2 inches). I don't think the end is at the midpoint tho. How do I figure out how long the arc length is?
My question involves being able to cut a round pipe into an arc that is 10 inches wide and 2 inches tall. I need to know the smallest diameter pipe to buy in order to fulfill these requirements.
Answered by Penny Nom. 





Sectors and arcs 
20060125 

From Wael: How is the area of an arc (alpha*pi*r squared/360) derived?
How is the length of an arc (alpha*pi*r/180) derived? Answered by Penny Nom. 





How would I find the length of the radius? 
20051015 

From Stace: If given the length of a chord (121") and the distance from the midpoint of the arc to the midpoint of a chord (12"), how would I find the length of the radius?
Answered by Penny Nom. 





The length of a circle's chord 
20050928 

From A homebuilder: find the length of a circle's chord with a known arc length and radius/diameter lengths. Answered by Penny Nom. 





Given only the length of an arc & the length of its chord find the radius? 
20050907 

From Robert: Given only the length of an arc (72) & the length of its cord (71), how to find the radius? Answered by Penny Nom. 





The radius of an arc 
20050819 

From Jared: I need to be able to calculate the radius of an arc on an existing structure (Supports for Fifth Ave Dimensional Text). I have the overall length of this structure, but, the complication I believe lies in the fact that it is a curve mounted onto a flat section of wall on either side of a very mild curve, therefore, measuring the middle of the wall to the top of the arc does me little good...The reason I need this is to be able to replicate the above curve on a similar structure to be mounted below it...Also, because the client wants the structure mounted on the inside of the opening below the existing, the beginning and end point of the new structure would be lower than the existing, so, I do not believe that it is possible to exactly replicate the radius of the above curve? Answered by Penny. 





Framing an arched wall 
20050812 

From Mike: I'm framing a building wall with a curved (arcing) top section. The radius of the section is 74'6" with a height above finish floor of 16'0". The horizontal run of the arced section is 23' 1 1/2" with a low height above finish floor of 12'4". If I start with a 16' stud at the high end how long are the subsequent studs if they are on 16" centers? Short of laying this out on a tennis court how can I work out the lengths of the studs? Answered by Penny Nom. 





arccos(5/13) 
20050531 

From Kyle: I would like to know how to evaluate the problem of: Arccos 5/13. Answered by Penny Nom. 





The volume of a sphere. Why 4/3? 
20050530 

From Lauren: You know when you find the volume of sphere? I know the formula is V= 4/3 pi r^{3} but why do they use 4/3? Answered by Penny Nom. 





Difference in latitude 
20050405 

From Gretel: Assuming the the earth is a sphere of radius 6378 kilometers, what is the difference in latitude of two cities, one of which is 400 kilometers due north of the other? 500 kilometers? Answered by Penny Nom. 





arcsech x 
20050210 

From Monica: Prove that arcsech x = ln[(1 + (1x^{2})^{(1/2)}) / x ] Answered by Penny Nom. 





Arcs and chords 
20050109 

From Aniesha: A chord of a circle is 48 centimeters long and is 10 centimeters from the center of the circle. Find the radius? Answered by Penny Nom. 





The gradiant of a hill is 9% 
20041218 

From Jim: The gradiant of a hill is 9%. What angle is created by the run/rise of the hill and 0 degrees? Answered by Penny Nom. 





A belt around two pulleys 
20041207 

From Ian: a belt is stretched around two pulleys whose centers are d units apart and whose radii are R and r respectively (obviously R+r<d). the challenge is to find the length of the belt, l as a formula in terms of R, r, and d only. Answered by Penny Nom. 





An arc of a circle 
20041205 

From Ruben: i have an arc 55 inches wide, 12 inches high at the centerline of the arc. how can i determine the diameter of the circle that would correspond to the arc. Answered by Penny Nom. 





The length of an arc 
20041121 

From Daryl: I am tying to find the arc length of a line 6' and the vertex of the arc 1' off of the line. that is all that is known Answered by Penny Nom. 





The radius of a circle 
20040824 

From Peter: If you slice any circle with a line, and call the distance of the line between intersections the "y" length and the perpendicular length to the shorter side of the curve the "x" length, what is the resulting equation for the radius? Answered by Penny Nom. 





The railing around a pool 
20040726 

From Bob: I have a 15' circular above ground pool. Around the perimeter of the pool are eleven (11) sections of railing. Each rail has 5 slots at each end for pins. I have calculated that the length of the arc under the railing to be 51.4". what I am trying to determine is the distance between the end points of the arc so that I can figure out which slot to use in the rails without going round and round the pool moving and removing the rails until they finally fit. Been there, done that, no fun. Answered by Penny Nom. 





The center of a circle 
20040526 

From Wan: I am trying to find the radius of an arc. The only things i know about the arc is all referenced from the line of tangency to the arc. on both sides i have a differnt horizontal perpendicular distance to the point of tangency.
left side * right side (*=point of tangency). Then i have 2 difference vertical perpendicular distance of the end points to the line of tangency. I know it sounds very bad in text but this is all i know about the arc. Can you help me find the radius? Answered by Penny Nom. 





Marching legion 
20040424 

From Art: A column of soldiers is 100 meters long. Their sargeant at the rear of the column gives the order to march. The sargeant marches alongside the column to its head and then back to the rear, at which point he gives the order to halt. In all, the column of soldiers has marched 100 meters. How far has the sargeant marched? I say 187.5 meters, but those who teach or who have taught mathematics tell me no. Some say much more and some different. What do you say? Answered by Penny Nom. 





An arc on a train track 
20040215 

From A student: I'm trying to build a route in a train simulator program. I have a curve to the right (an arc, in other words) with a length of 25 meters and the radius is 1,500 meters. Let's say point P is the beginning of the curve (arc) and point Q is the end point of the arc. Then picture a tangent to point P. I need to find the length of a line perpendicular to that tangent that runs to point Q (the end of the curve/arc). Answered by Penny Nom. 





A parabolic arch 
20040119 

From Teresa and Robyn: A bridge over a river is supported by a parabolic arch...arch is 200 m wide at water level...the maximum height of the arch is 80 m..what is the height of the arch measured from a point on the water 40m from the centre of the arch Answered by Penny Nom. 





The length of a chord 
20031103 

From David: When Radius=400.00' and Arc=130.58' what is the Cord distance in feet? Answered by Penny Nom. 





An arc of a circle 
20030312 

From Melissa: A strip of wood is 16 ft. long and is bent in the arc of a circle. Two radii, from the center of the circle to the ends of the arc, form a right angle. What is the approximate distance from one end of the wooden arc to the other? Answered by Penny Nom. 





The length of an arc 
20030224 

From Gavin: does anyone have a formula for calculating the length of an arc if I have the circle radius and the cord length of the arc?? Answered by Penny Nom. 





The length of an arc 
20021127 

From Nancy: If all I have is the length between 2 ends of an arc (72"), how do I find the length of the arc at its apex and the radius? Answered by Penny Nom. 





How would you find the length of the chord? 
20021031 

From A draftsperson: If given the length of an arc and the distance from the midpoint of the arc to the midpoint of a chord, how would you find the length of the chord and the radius of the arc. The chords endpoints are the same as the the arcs endpoints. Answered by Penny Nom. 





x^{ 4} + x^{ 5} = 100 
20021027 

From Bill: One of my students has stumped me. He asked how to solve the equation 4^{ x} + 5^{ x} = 100 All I can think of are graphing methods to get an approximate solution. What am I missing? Answered by Harley Weston. 





A cone that is cut off at the top 
20020923 

From Stuart: I have to work out the dimensions and arcs of a cone that is cut off at the top. I.e Top diameter is 33mm to bottom diameter is 43mm and the depth is 80mm Are you able to work what the flat of this cone would be as I need to design within the flat area and then have it cut out. I really need to know what the flat of it is before it is cut and curled to form the above cone. Answered by Walter Whiteley. 





3 radians subtends an arc of 27 meters 
20020522 

From Kyle: In circle O, a central angle of 3 radians intercepts an arc of 27 meters. Find the number of meters in the length of the radius. Answered by Penny Nom. 





Arc length 
20020417 

From Vix: Find the point on the curve r(t)=(12sint)i(12cost)j+5tk at a distance 13pi units along the curve from the point (0,12,0) when t=0 in the direction opposite to the direction of increasing arc length. Answered by Harley Weston. 





Arclength of an ellipse 
20010703 

From A hobbyist: What is the equation (with the length of the arc as a variable) for one quadrant of the ellipse,... Answered by Claude tardif. 





Arc of a sphere 
20010304 

From Some students: My friends and i have a geometry project and we cannot seem to figure out how to find the arc of a sphere. Answered by Harley Weston. 





cot(arcsin 3/5) 
20010107 

From Jason: Find value. Assume that all angles are in Quadrant 1. cot(arcsin 3/5) Answered by Harley Weston. 





Bridges and parabolas 
20001118 

From Lauren: My name is Lauren, and Im a secondary school student in Ontario. For my gr11 advanced math class I have to find out how and why parabolics are used in arch bridges and write 3 paragraphs on it. People who cohse satelites and whatnot are lucky  I've found a ton of info, but for arch bridges there seems to be nothing. Answered by Harley Weston. 





Cairo tesselation and Archimedean duals 
20000621 

From Joyce DuVall: I am looking for a picture of the Cairo tesselation, and pictures of the Archimedean duals. Do you know of any good web sites or books? Answered by Penny Nom. 





Calculus Research Questions 
20000522 

From William Wright: I am a Calculus Teacher, and me and my class ran into these two problems without solutions in my manual, we got answers, but are unable to check them. If anyone gets this email and can respond to this with the solutions it be greatly appreciated. . . . Answered by Harley Weston. 





Volume of a sphere 
20000521 

From Kevin Partridge: Does anyone have a way to physically demonstrate how to explain the volume formula for a sphere? Or perhaps how to derive the formula without calculus? Answered by Harley Weston. 





A problem with a radius. 
20000201 

From Howard B Davis: We start a Line that goes up 1 unit, then it goes to the Right for 5 units long, and then goes down 1 unit which is the end point. If we draw a circle that is tangent to both ends as well as the midpoint of the horizontal line: How do we find the radius of the arc; in Mathematics, with only this information? Answered by Chris Fisher. 





Arclength of a circle 
20000119 

From Holly: What is the formoula for finding the arc length of a central angle of a circle?? Answered by Harley Weston. 





A roll of paper 
20000115 

From Richard: I have a roll of paper, wrapped around a corrugate core, whos diameter is 10.750 in. The outer diameter of the roll is approx. 60 in. The thickness of the paper is .014 in. I am trying to find out how much linear feet of paper is left on the roll, given only the diameter of paper remaining on the core. Answered by Chris Fisher and Harley Weston. 





Length of a line 
19991010 

From Dagmara Sarudi: My question has to do with the length of a diagonal. This problem came up when I thought about the shortest distance between two points, for example walking from one point to another in my neighborhood. I can choose a zig zag route and assuming the blocks I walk are exactly the same length, it shouldn't matter what route I took, the distance I travel should still be the same when I reached my goal. If, on the other hand I could travel in a diagonal line, the distance would be shorter. But what if, in my zig zag motion, the sections get so small the route approaches a diagonal. Shouldn't it be that each separate section added together equals the value of the two original sides? Or would it suddenly equal the value of the diagonal (which, of course was shorter than the two sides added together)? What gives? Answered by Chris Fisher and Harley Weston.






Radius of an arc 
19990422 

From Rusty Riddleberger: I need to find the equation for finding the radius of an arc; I know the length of the arc (i.e the distance of the line connecting the two ends of the arc) and the height; (i.e the rise of the arc at its apex,) I had the formula years ago but it has lost me; this would be invaluable for work in new homes i.e. where we need to build an "arch" with a rise of 21" between two columns 11 feet apart Answered by Chris Fisher. 





Linear programming and optimization 
19990409 

From Shams: What is Linear programming and optimization? Answered by Jack LeSage and Penny Nom. 





Operations Research 
19981008 

From Lisa Barrett: What is the history of operations research and the study of linear programming? Answered by Judi McDonald. 





The Earth's Arc 
19980206 

From Robert Dyck: How do I find the arc/mile of the earths surface? What is the arc? Answered by Harley Weston. 





A problem with arccos. 
19970609 

From Vanessa Chan: Prove: arc cos4/5 + arc cos (5/13) = arc cos (56/65) Answered by Harley Weston. 





Approximating pi. 
19961104 

From Ben Dixon: How do you calculate Pi? Do you have to somehow combine the equation for a circle with the formula for the circumference? Answered by Chris Fisher. 





Solides d’Archimède 
20140429 

From Clémentine: Pourquoi une pyramide a base carrée n'est elle pas un polyèdre archimedien ?
J'ai pourtant essayé d'en construire un avec tout ses cotés égaux et ça fonctionne !
Aidez moi je n'en dors plus la nuit ? :S Answered by Chris Fisher. 





Un bénéfice de 5% 
20080311 

From mahiques: Un propriétaire decide de vendre deux parcelles de terrains pour un montant total de 141750 F. Il fait un bénéfice de 15% sur la première et une perte de 10% sur la deuxième. L'ensemble de la transaction lui a rapporté un bénéfice de 5%.combien atil vendu chacune des parcelles ? Answered by PierreLouis Gagnon. 





Le salinon d'Archimèdre 
19990311 

From Don Craig: I am trying to find the English translation of "Le salinon d'Archimèdre" and would appreciate any help. This is a figure, presumably studied by Archimedes, created from 4 semicircles. Since I can't draw it for you, I will try to describe it with the help of the 5 collinear, horizontal points below. . . . . . A B C D E A semicircle is constructed on AE as diameter (let's say above AE). Two more semicircles are then constructed with diameters AB and DE on the same side of the line AE as the first semicircle (above it). Finally, a fourth semicircle is constructed on diameter BD, this time on the opposite side of the line AE from the others (i.e. below the line). These semicircles and the region enclosed by them constitute what is called in French "Le salinon d'Archimèdre". If you know the English name of this curve I would appreciate it if you let me know. Answered by Harley Weston. 

