







The length of a train 
20170424 

From Stefano: If a freight train is coming towards you and you were traveling at 85 miles an hour and it takes 35 seconds for the train to pass you how long is the train
Figure 50mph for train Answered by Penny Nom. 





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. 





The lateral side length of a cone 
20160605 

From Diane: Question is find the lateral side length of a right cone with area of 372 sq. cm and base circle radius of 9 cm. 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. 





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 length of an 80 acre piece of land 
20160121 

From Eugene: Have to clear a piece of land 80 acres by 500 feet wide. What is the length of the property? Thanks Gene Answered by Penny Nom. 





The perimeter of a one quarter acre square 
20160115 

From Kerry: If you have a perfect square that is one quarter of an acre what are the length of the sides and how do you arrive at the solution? thank you, Kerry. Answered by Penny Nom. 





The length of a rectangle 
20150926 

From Tris: Hi,
I'm trying to figure out the length of a rectangle but i forgot how. So, the width is
5cm and the perimeter is 34cm. Answered by Penny Nom. 





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. 





An octagonal frame around a pool 
20150517 

From James: I have a 20' pool and need to put a frame around it using 2by 4 what r the lengths and angle cuts Answered by Penny Nom. 





The side length of a gazebo 
20150314 

From Dennie: From middle of side to middle of opposite is 14'6". What is the length of the side? Answered by Penny Nom. 





6 bolt holes around a circle 
20141026 

From Bobby: What Is The Cord Dimension For 6 Holes On A 24" Bolt Circule 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 octagon around a tree 
20140716 

From floyd: I want to build an octagon 4 feet from base of tree from 4x4's. What length do I cut my pieces 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. 





The length of a shadow 
20140509 

From vijay: A girl of height 80 cm is running away from the base of a lamppost at a speed of 2 m/s. If the lamp is 4 m above the ground, find the length of her shadow after 5 seconds. Answered by Penny Nom. 





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 side lengths of a triangle 
20130107 

From Katie: How do I find the side lengths of a triangle knowing the base and its height?
Thank you, Answered by Penny Nom. 





The length and depth of a chord 
20120816 

From Tim: Can I find the radius of a circle, if I have a chord of 2400mm, and a depth
between the center of the chord and the perimeter of the circle of 150mm ?
Thanks
Tim Answered by Penny Nom. 





Two altitudes of a scalene triangle 
20120813 

From grace: Two of the altitudes of a scalene triangle ABC have length 4 and 12. If the length of the third altitude is also an integer, what is the biggest that it can be? Justify all of your conclusions. Answered by Chris Fisher. 





An octagonal sandbox around a pool 
20120612 

From Linda: My pool is 15 feet across and it is round.
How do I measure to cut wood to build a sandbox around it? was thinking it will look like an octagon.
Thanks Answered by Harley Weston. 





How to find the base length of a isosceles triangle if only the sides are given? 
20120425 

From aqilah: how to find the base length of a isosceles triangle if only the sides are given? Answered by Chris Fisher. 





A rectangular prism 
20120405 

From Tori: How do you find the base height if the base width is 10ft. The height is 7ft. And the volume is105ft. Answered by Penny Nom. 





Forming a triangle from 3 line segments 
20120315 

From rustom: A point X is selected at random from a line segment AB with midpoint 0. Find the probability that the line segments AX, XB, and A0 can form a triangle. Answered by Penny Nom. 





A 23 acre airport runway 
20120221 

From Ron: I have a 23 acre plot. If it were in a straight line, would it be enough distance for a plane to take off and land if the plane needed 1 mile? Answered by Robert Dawson and Penny Nom. 





The dimensions of a rectangle 
20120106 

From joseph: The perimeter of a rectangle is 72 inches. The length of the rectangle
is three more than 2 times the width of the rectangle. What is the
length of the rectangle? Write and solve an equation to determine the
dimension of the rectangle. Answered by Penny Nom. 





Three sides of a triangle 
20111224 

From saba: the three sides of a triangular lot have lengths 10,11and 13cm,respectively.
find the measure of its largest angle and the area of the lot? Answered by Penny Nom. 





The sides of a regular octagon of area 800 sq. ft. 
20110921 

From Susan: Help please. I am building an octagon tree house to live in. I would
like the total square footage to equal 800 to 1,000 sq ft. How long
should each side of the octagon be.
tx, susan 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. 





The length of a belt around three pulleys 
20110518 

From Grant: I need to calculate the belt length around these pulleys, please can you
help or refer me?
Known variables
D  Large Pulley Diameter
d  Small Pulley Diameter
c  Center Distance between D and d
T  Tension Pulley Diameter
x  Horizontal Distance between T and d' Centers
y  Vertical Distance between T and d's Centers
I need to calculate the belt length around these pulleys.
Kind Regards,
Grant Answered by Harley Weston. 





The length of a chord 
20110425 

From G: A 120 degree central angle intercepts a circle at the points A and B. The radius of the circle is 10 cm. Find the length of chord AB. Answered by Penny Nom. 





Triangles with perimeter 16 cm 
20110222 

From Chong: How many triangles (up yo congruence) with perimeter 16 cm and whose lengths of its side are integers? Answered by Chris Fisher. 





The sides of an equilateral triangle 
20110127 

From Cristal: Hello :) How can i find the sides of an equilateral triangle when only given the height 10m? Answered by Penny Nom. 





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. 





A 20" octagon 
20101119 

From CHARLES: I have a 20" octagon and it has 8 parts. In inches how big is each
part. I was told each part was 5.86".The top of the octagon breaks
into 3 equal parts don't equal 20".When i did my math i thought it should be 6 5/8" which is closer
to 20"
I am trying to cut a octagon out of a 20"circle Answered by Stephen La Rocque. 





The sides of a trapezoid 
20101103 

From Bobbi: Isosceles Trapezoid base=60”; two 45⁰angles at base, two 135⁰ angles at the top, vertical distance between base & top=16”. What is the length of the top line and the two equal side lines? Answered by Penny Nom. 





The length of a vector 
20100912 

From kyrie: Find the possible values of the constant a such that
 ai + 4aj + 4k  = 13
I know the answer is 3 but not sure how to get to it Answered by Penny Nom. 





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. 





A roll of paper 
20100325 

From keith: how many yds of paper for a roll with a width of 6.875 and a core of 3 in and a diameter of 40in? 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 side length of a square 
20100308 

From tara: am trying to help my brother's daughter in maths, tomorrow she has maths exam
1. Area of sq. picture is 441 sq.cm what is the length of its side. Answered by Penny Nom. 





What is the length of my sidewalk? 
20100127 

From Les: Name: Les
Who are you: Student
I have a sidewalk 4"thick,4ft. wide,and I have 2cubic yards of concrete. What is the length of my sidewalk? Answered by Penny Nom. 





The length of a sidewalk 
20100119 

From Les: I have a sidewalk 4"thick,4ft. wide,and I have 2cubic yards of concrete. What is the length of my sidewalk? 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. 





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. 





The length of tape on a reel 
20090806 

From Philiip: What diameter reel would be required to roll up 1000 meters of tape that is 0.01 mm thick such that the final role left 10 mm empty space between the top of the roll and the outside of the reel, the hup that the tape was wound on was 2 cm? 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. 





Height of a Flag Pole 
20090626 

From Jake: Can anyone answer this I am very stumped.
The flagpole on the roof of a Chocolate Factory is 13 cm in diameter and
a perfect cylinder. If one end of a 2300cmlong string is attached to the top
of the flagpole, and wraps around the flagpole exactly 16 times before ending
at the bottom of the flagpole, how tall is the flagpole? Need answer by Wednesday Answered by Penny Nom. 





Thermal Expansion of Steel 
20090617 

From Ken: Hi there, We are rollforming steel roofsheeting in 65M lengths and the =
question of linear expansion has cropped up.I would like to know what =
the expansion rate of this sheet would be over a temperature rise of say =
40degree F.in mm per Meter or whatever the norm is. The sheet is 0.53mm =
thick and is 700mm in width,I hope this is sufficient info to enable you =
to do your calculation.Many thanks, in anticipation.
Ken Answered by Janice Cotcher. 





Linear feet into Square feet 
20090604 

From Vickie: Hoe do I change 10 linear feet into square feet? Answered by Janice Cotcher. 





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 length of a ladder 
20090330 

From Susan: The foot of an extension ladder is 7 ft. from a wall. The height that the ladder reaches on the wall and the length of the ladder are consecutive integers. How long is the ladder? 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. 





The length of a chord 
20090320 

From shirley: show that the chord is equal to two times the radius time the sin of theta/2.
The chord is connected to the two radii and theta is a central angle between the two radii Answered by Penny Nom. 





Related rates 
20090314 

From Jeevitha: The side of an equilateral triangle decreases at the rate of 2 cm/s.
At what rate is the area decreasing when the area is 100cm^2? Answered by Stephen La Rocque. 





The sides of a triangle 
20090307 

From felicia: ona map, tannersville, chadwick, and barkersvile for a triangle. Chadwick is
70 miles from Tannersville and Barkersville is 90 miles from Tannersville. Which is a
possible distance between Chadwick and Barkersville?
a. 5miles
b. 10 miles
c. 150miles
d. 200 miles Answered by Harley Weston. 





The sides of a polygonal building 
20090213 

From mark: length of sides of an 18 ft.diameter bldg
i need to find out if i should build an octagon or decagon to keep the
sides of the bldg at 8ft or less. how do i figure the length of the sides
of each? Answered by Penny Nom. 





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. 





One acre of land 
20090131 

From michelle: Can you tell me how many feet in length would it be for a acre if the land is 155 feet wide.
Thank You! michelle Answered by Penny Nom. 





A standard bill on a highway 
20081219 

From Stephanie: A standard bill on a highway has a perimeter of 14 feet. the length of the bill board is 6 feet greater than triple the width.
What is the length?
what is the width? Answered by Robert Dawson and Penny Nom. 





The sides of an octagon 
20081012 

From side lengthsGarry: I need the length of the sides and the degrees of the angles for a 30 inch diameter
octagon Answered by Janice Cotcher. 





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 sides of an octagon 
20080921 

From mark: I need to know the measurements of an octagon with a inside diameter of 34.5 inches from side to side Answered by Penny Nom. 





The length of a pipe 
20080825 

From John: How many feet of one inch pipe would it take to hold 30 and 40 gallons of water?
Imperial gallons please. Answered by Penny Nom. 





Arclength and sectorangle 
20080806 

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





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 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. 





The length and width of a rectangle 
20080611 

From gregg: the perimeter of a rectangle is 70 feet. the ratio of length to width is 4:3. how would i calculate the length of the height and width? Answered by Penny Nom. 





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. 





The area of a regular pentagon 
20080602 

From Jenna: I would like to know if there is a formula to find the area of a regular Pentagon that is not inscribed in a circle only apothem and side length are given. Answered by Penny Nom. 





One chord is twice as long as another 
20080530 

From Stacey: In a circle, If one chord is twice as long as another, is the longer chord's arc also twice the size of the smaller chord? True or False Answered by Chris Fisher. 





Find a way to represent the length and width of the box. 
20080525 

From Angela: The volume of a box that is two inches high can be represented by V=2X^220x+32. Find a way to represent the length and width of the box. (Hint: you will need to use factoring). Answered by Stephen La Rocque. 





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 fourth side of a property 
20080514 

From Penny: Property has 3 measurements and 2 angles and I want the altitude at a particular point. Corners are sw, nw, ne and se. 1 want the 4th saide measurement confirmed (we think 146.07') and the altitude measurement at 25' from sw (on the swse side)
The angles provided are interior at nw 67.38 degrees and the opposing corner se interior appears to be 68.58 degrees. the 3 sides with measurements are: sw to nw=54.07'. sw to se 146.07' and se to ne 53.57'. If you would help, we would really appreciate it. Thanks! Penny 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. 





The sides of an octagon 
20080507 

From Frank: Question from Frank, a parent:
Hi,
Need to lay out a 10 ft. diameter octagon on the ground. What is the
length of the
sides ? And the angles ? Answered by Harley Weston. 





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. 





Side lengths and angles in a regular octagon 
20080409 

From Lori: I am a builder and need to find the length of the sides of an octagon. I know the length between
the parallel sides (26 feet). What is the length of each side? What is the angle measurement? Answered by Harley Weston. 





The length of a side of a square 
20080312 

From laura: if i had a square of 2.3 square meters what would its radius be?(in centimeters please) Answered by Penny Nom. 





A widthtolength ratio of 2 : 3 
20080311 

From Stephanie: The national flag of France has a widthtolength ratio of 2 : 3. What is the width of an 18inch long French flag? Answered by Penny Nom. 





Side lengths and area of a triangle 
20080308 

From angela: In the diagram of ABC the angle A is 65 the angle B is 70 and the side opposite vertex B is 7. Find the length of the side opposite vertex A and find the area of ABC Answered by Penny Nom. 





A roll of paper 
20080305 

From Sheik: How I Convert My Roll Weight Into Meters?
Roll Width : 241mm
Thickness : 56gsm
Weight :81 Kg Answered by Harley Weston. 





The dimensions of a rectangle 
20071212 

From tara: The length if a rectangle is 5 feet less than twice its width. The perimeter of the rectangle is 38 feet. let w represent the width. write an equation for the perimeter of the rectangle in terms of w. Then solve the equation to find the length and width o the rectangle. Answered by Penny Nom. 





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. 





Area and side length of a hexagonal tent 
20071009 

From Mark: Trying to buy a tent with 6 sides, in the catalog they give me sq. ft., what is the distance from side to side of a hexagonal tent with an area of 90 sq. ft. 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. 





Proof that any side of a triangle is less than half the perimeter. 
20070707 

From Omkar: Any side of a triangle is smaller than half of its perimeter, prove this in short ? Answered by Stephen La Rocque. 





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. 





Area of a hexagon (three ways to find it) 
20070524 

From Josh: I have to work out the area of a hexagon when I know that the perimeter
of it is 1000m. I have tried many different ways but I get different
answers. Answered by Stephen La Rocque. 





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. 





The length of the side of a hexagon 
20070219 

From Nick: if the area of a regular hexagon is 259.807 how do i find the length of each side, and the apothem? thanks if you can help Answered by Penny Nom. 





Chord length 
20061101 

From Tony: how do i find a chord length when all i have is arc length (13.633m) and the radius (89.500m) Answered by Stephen La Rocque. 





Determine the width and height 
20061012 

From Roshawn: If I am given the length of 73" and the girth of 11" and am trying to determine the width and height. How would I do this? Answered by Stephen La Rocque. 





Two word problems 
20061002 

From Eve:
1. A surveyor's map shows a plan for the rectangular rose garden whose area is
a^{2}+25ab350b^{2}. Find an algebraic expression for the length and width. If a=20 ft and b=10 feet, find the actual dimensions of the garden.
2.A square is enclosed in a circle. The area of the square is (4r^{2}32r+64)sq cm and the area of the circle is 484r^{2} sq cm. Write a polynomial in factored form to represent the difference of the two areas.
Answered by Stephen La Rocque. 





The length of 2 sides of a triangle 
20060915 

From Lonnie: I need to know how to figure the length of 2 sides of a triangle, as the following example:
The length of the bottom is 12' and the angles are 45, 45 I need to know how long the other 2 sides must be to get an angle of 90 at the top. Answered by Stephen La Rocque. 





Calculating the belt length of a three pulley system 
20060716 

From Mark: I have a 3 pulley system with sides abc and pulleys ABC. Pulley A has radius of 10cm, pulley B has radius of 20cm, and pulley C has radius of 3cm. The side lengths are: (center to center of pulleys) between pulleys AB = 75cm, between pulleys BC = 100cm, and between pulleys AC = 50cm. I set these side lengths up as (according to law of sines and cosines) a = 100cm, b = 50cm, and c = 75cm. What is the length of the belt required for this system? I need to know how I would set this problem up and solve. Answered by Stephen La Rocque. 





Finding square footage from lengths in inches 
20060714 

From Ann: How do I find out the square footage of a window 45" by 22" and 43" by 35.5"? Answered by Stephen La Rocque. 





An octagon shape flower bed 
20060624 

From Brandy: hello my name is brandy my husband and I would like to build an octagon shape flower bed to put around the tree in the front yard
we would hope to have the whole shape about 4 ft5 ft around the tree. what would be the way to find out how to cut each side to that they fit together equally Answered by Penny Nom. 





A side segment of an octagon 
20060624 

From Ed: I would like to know how to find a side segment of an octagon when I know that my octagon is 9 feet from side to side and top to bottom? Answered by Stephen La Rocque. 





The chord length of a polygon 
20060614 

From Krishna: I have to find out the chord length of a polygon  Tetradecagon ! The Radius of the Circle is 11.5 Cms. The Circle is intersepted by 14 arcs. Then how to find out the chord length? Answered by Stephen La Rocque. 





How long and how wide is the table? 
20060202 

From A student: the perimeter of a table is 24 feet. the table is twice as long as it is wide. how long and how wide is the table? 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. 





The length of a chord 
20051103 

From Sue: How do you determine the length of a chord when given the diameter of the circle (1.6m) and that the angle = 7π/8 Answered by Penny Nom. 





The sides of an octagon 
20051102 

From Royce: I understand there is a simple calculation to determine the sides of an octagon when you know the distance across the parallel flats. something like .447 . can you help? 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. 





The length of the side of an octagon 
20050922 

From Billy: How can you find the length of the side of an octagon when all that you know are the long sides of one of the eight perfect isc. triangles inside the octagon that share the same center point? Answered by Penny Nom. 





The length of a chord 
20050908 

From A student: how do you find the length of a chord given the angle and radius of the circle 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 length of a whale 
20050604 

From Judy: A whale's head is 72 inches long... its tail is as long as its head plus half the length of its body, and its body is half the entire length. Who long is the whale? Answered by Penny Nom. 





Th dimensions of a garden 
20050209 

From Rebecca: Nate's garden has a perimeter of 34 meters and an area of 72 square meters. What are the dimensions of the garden? 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 length of a rectangle 
20040926 

From Rebecca: My question is each side of a square S is 18 inches long and the area of S is at least 3 times the area of a rectangle that is 9 inches wide. What is the greatest possible length in inches of the rectangle? Answered by Penny Nom. 





The length of a cut 
20040917 

From Florita: My daughhter, who is a 9th grader is attempting to cut a piece of wood after determining the length of the cut for the hypotenuse. These are the measures:
a=4squared, b=6squared.
She determined that c should equal 52. But when she measured the actual piece to be cut, c measured 39.5 inches! Can you offer any insight as to what she is doing wrong? I have suggested that she may be working with an Acute rather than a Right angle . But she insists that it is a Right angle after using a "framing square". Answered by Claude Tardif. 





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. 





Two vector problems 
20040714 

From Jaye: Two force, 120lb and 200lb, act on a body and make a 52 degree angle w/ ea. other. What's the magnitude of the resultant of the forces and what is the measure, to the nearest degree, of the angle that it makes with the 200lb force? Answered by Penny Nom. 





The dimsenions of a room 
20040518 

From Estella: I have a room that is rectangular the area is 159.5 feet, the perimeter is 51 feet what would the dimensions of the room. Answered by Penny Nom. 





Laying decorative bricks 
20040107 

From Duk: Loren is laying decorative brick along both edges of the 21meter walkway up to his house. Each brick is 0.26 meters long. He is placing the bricks end to end. How many bricks does he need to do the job? Answered by Penny Nom. 





The side length of a regular octagon 
20030809 

From Rich: If I know the distance between the parallel lines of an octagon and want to find the length of the sides, can I just divide that distance by 2.414 to reveal the length of the sides? I work construction and just curious if I am figuring it right. Answered by Penny Nom. 





The length of fabric in a roll 
20030703 

From Paul: We receive rolled fabric as part of our process and I would like to know is there a formula that could be used to estimate the overall length of the roll with out rolling the fabric out and measuring its length. Answered by Harley Weston. 





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 dimensions of a box 
20021203 

From Paula: My son, who is in secondary school, needs to make a box with the inside dimensions of 1.25 cubic feet. It's supposed to be more in the shape of a rectangle than a square. I would like to know the equation to use to find the inside dimensions of a box if I know how many cubic feet (or inches) I need the inside to be. 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. 





An equalateral polygon inscribed within an ellipse 
20020630 

From Steven: How would you calculate the length of one of the sides of an equalateral polygon (of n sides) inscribed within an ellipse ( of any eccentricity ) where all of the vertices exactly touch the perimeter of the ellipse? I know that when the eccentricity is zero ( i.e a circle ) the formula: r * (sin(180/n) * 2) will suffice. But what about when the eccentricity is greater than zero? Answered by Chris Fisher. 





Chord length 
20020517 

From Ashlie: How do you find the chord length of one section of a chord if you only have the diameter length and the other whole chord length. WV is the diameter and equals 16. XY is perpendicular to it, and equals 10. They intersect at pt. Z. I need to know what WZ equals. Please help! 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. 





An octagonshaped deck 
20020220 

From An instructor: How can you solve for finding the side measurements of an octagonshaped deck that is 10 feet long and 10 feet wide. Answered by Penny Nom. 





Third side of Acute Triangle 
20011109 

From Don: I gave this problem to my children, 9th and 12th grade and they are not(me too!) sure of the answer. I am trying to determine the length of the third side of an acute triangle. I know two of the lengths but I do not know the angles. Is there a proper formula to use to find the length of the third side? Thank you. Answered by Chris Fisher and Penny Nom. 





Fourier transform 
20010807 

From Adbul:
 Sir, we have the Dirichlet's condition for the Fourier transform : " The function should be integral over the real line " But why we are we neglecting this for example when we take the Fourier transform of an impulse train?
 Suppose we want to travel from one corner of a square of side 'a' to the diagonally opposite corner. We can travel along the sides which gives a pah length of '2a'. We can also do it in steps as shown below:
_  _PATH  _ _____
Suppose The step size =DELTA x Then the path length will be again '2a'. Now in the limit DELTA x >0 again we get '2a' But when we take the limit we get the straight line diagonal whose length is 'SQRT(2)X a' Where did I go wrong? Answered by Chris Fisher. 





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. 





The sides of an octagon 
20010413 

From Craig: How do I figure the length of the sides of an octagon when all I know is the diameter (4.375). Answered by Penny Nom. 





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. 





Rotation 
20010125 

From A student: If I have a rectangle 2inches long and 4 inches wide and I rotate the rectangle 45 degrees will the length still be 2 inches? Answered by Penny Nom. 





The magnitude of a complex number 
20001111 

From Jeremy: Recently, we started studying how to graph complex numbers. Our math teacher said to use what would normally be the xaxis as the realaxis and to use the yaxis as the imaginaryaxis. However, when he started talking about how to calculate magnitude, that's when I became confused. For instance... Answered by Walter Whiteley. 





Length of a shadow 
20001101 

From Jessy: A man who is six feet tall is walking away from a street light that is fifteen feet tall. How long is the man's shadow when he is ten feet away from the light? Answered by Penny Nom. 





A chord length 
20001017 

From Al Paas: How to determine the length of a chord given the diameter of the circle and the maximum distance from the chord to The circle? Answered by Chris Fisher. 





The smaller of a and b 
20000914 

From Jenna: For any two real numbers, a and b, give a mathematical expression in terms of a and b that will yield the smaller of the two numbers. Your expression should work regardless of whether a>b, a Answered by Penny Nom. 





Side length of an octagon 
20000422 

From Unknown: If I have an octagon that is 12 feet across (side to opposite side) how can I find the length of the sides? Answered by Harley Weston. 





History of a meter 
20000407 

From Jarod Fischer: The length of a meter has been determined in three different ways. The first and original way was determined in 1798. The second way was determined in 1960. The third and current way was determined in 1983. What were the three ways and why were the first two abandoned? Answered by Harley Weston. 





The side length ratios of some triangles 
20000404 

From Alexis Lockwood: I am doing a project for my Math 30B class regarding the side length ratios of 454590 degree and 306090 degree triangles. I would really appreciate any assistance in answering the following questions, or even direction to an appropriate web site or resource on the matter. Answered by Harley Weston. 





Pi 
20000222 

From Shelley Collier: Numbers that can be written in the form p/q where p and q are integers, (q not 0), are known as rational numbers. What you are missing is that p and q must be integers. The fact that Pi is irrational means that you can't have a circle with both the circumference and diameter being integers. In fact you can't even have the circumference and diameter both rational since the quotient of two rationals is again a rational. Answered by Claude Tardif and Penny Nom. 





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.






Perimeter 
19990815 

From Mel Nordan: The length of a rectangle is IS 3 1/2 times its width. Its perimeter is 108cm. Find its length and width. Choices for the width: 12,18,24 Answered by Penny Nom. 





Measuring the fourth dimension 
19990607 

From Suzanne Hall: Hi! The other day, two of my students asked a very interesting question: Is the fourth dimension measured with hypercubes? Their reasoning went like this: Lines are 1D and are measured with line segments, which are part of a line. Planes are 2D and are measured with squares, which are part of a plane. Space is 3D and is measured with cubes, which are part of space. So, logically, hypercubes would be used to measure the fourth dimension. Answered by Chris Fisher. 





Girth 
19990526 

From Carolyn Bulkley: I am trying to explain to my son (who is in the 8th grade) how to figure girth. I'm afraid I have just confused him. Is there a simply formula to figure the girth of a box. for example: I have a box that is 27" L X 22" W X 21" H. Answered by Penny Nom. 





The bricklayers formula 
19981124 

From Rachel Kaplan: I have to do a report on the bricklayers formula N = 7LH. Can you give me any information on this. Answered by Harley Weston. 





A Hexagon 
19980922 

From Lee Curtis: Could someone calculate this for me? If a hexagon is 38 feet 8 inches across, how wide would each of the six sides be? Thank you, Lee Curtis Answered by Chris Fisher and Harley Weston. 

