







An octagonal pool deck 
20200530 

From lauchie: need help on cut sizes and cut degrees on octagon pool deck for a 24 foot round pool Answered by Harley Weston. 





The side length of a hexagon 
20200205 

From Rob: I have a hexagon that is 8 feet wide how long would the sides be? Answered by Penny Nom. 





The angle of a countersunk screw 
20200119 

From Barbie: I need to be able to verify the angle used for the head of a countersunk screw.
I have the diameter of the head, diameter of the shank and height between the
two. I assume it would be considered a frustum.
For example:
A standard 90 degree metric flat head screw in an M2 diameter has a head diameter of 3.65mm,
the actual thread diameter is 1.98mm and the height of the head is 1.20mm.
How can I prove that it is a 90 degree angle? Answered by Harley Weston. 





A hexagonal planter 
20191119 

From Colleen: I need to build a hexagon planter around a 32” square box. How long is each side of the hexagon? Answered by Penny Nom. 





A tube through a board at 45 degrees 
20190615 

From Guy: I need to insert a tube 5/8" diameter into a board at a 45 degree angle. What size hole must I drill for the tube to fit snugly? Answered by Harley Weston. 





Subdividing land 
20190509 

From Reuben: This is the measurements of my plot, AB 46.7M, BC 193.1, CD 198.5 & DA 208.25 (Clockwise naming of sides) angle A at 90 degrees. My questions is how do i subdivide this plot from the bottom having lines running parallel to CD, eg two 2acre plots. the the remaining part becomes my compound (Uper part at line AB) Answered by Harley Weston. 





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. 





Roof Square footage 
20151111 

From Todd:
Question from Todd:
Good Day.
I have to figure out the square footage of a quonset style roof that's not playing by the rules The building dimensions (rectangular) are 63'x135' the height of the roof is 9.25'. It not an entire Quonset, It's that style of roof,(curved). There are concrete block walls 10' up to the metal roof.
Thank you!
Todd Answered by Harley Weston. 





A fishfinder 
20150313 

From Dave: I have a fishfinder that has a 20 degree cone on bottom of boat going to the bottom of the lake.
How do I know the size of base diameter of the cone on the lake bottom depending on depth...
such as 10 feet deep, for example? Answered by Penny Nom. 





The length of a ramp 
20150305 

From Jaylynn: Hi, I've been trying to figure out how long my ramp would have to be in order to reach a height of 3.5 feet at a 30 degree angle for a sugar glider enclosure? Answered by Penny Nom. 





Bricks around a fire pit 
20150305 

From Jayson: I have a round fire pit. It measures 25 inches in diameter. I have 12 inch long square bricks to go around it . My question is what degree do I cut the ends of these bricks to make them fit around this circle? The brick dimensions are 12"Lx6"Wx4"D. Answered by Harley Weston. 





Cutting a round cake so that it doesn't dry out 
20140826 

From James: I'm wondering if there's a simple way to calculate the area between two parallel chords of a circle equidistant from its diameter, or if I have the area, to find the distance between the two chords.
Here's my "problem". You may have heard of the way of cutting a round cake so that it doesn't dry out  make two parallel cuts (chords) the length of the cake, take the middle piece, then push the two pieces together.
So I know the area of a 12" cake, and I want say, exactly an eighth of the cake. How wide do I cut the centre piece?
Now to get even more difficult, the next day I want another eighth from the centre. How wide do I cut the next pieces, and so on...?
Thanks,
James Answered by Harley Weston. 





An octagonal pad 
20140425 

From George: Hi,
I need to pour a cement pad in the shape of an octagon that allows
for 12" of clearance around the tank I will be putting on it.
The tank has a radius of 16'. Answered by Penny Nom. 





Cutting a hexagon from a disk 
20140405 

From Paul: I am a machinist and sometimes need to make a hex from
round material.
If I know the distance of the flat sides opposite one another
of my hex, how can I calculate the size of material I need to turn
to give me the right diameter to finish the part with six sides? Answered by Penny Nom. 





The area of a 5 sided lot 
20140315 

From Michael: Question from michael:
This lot is in feet. 59x154x109x188x137 per the plot plan Answered by Harley Weston. 





conical lamp stand/staved wood 
20131207 

From Henry: need to make lamp stand that is wooden staved; need it to be 25 inches at bottom and 10 inches at top; need to know angles for staves to be cut; the lamp stand will be rounded on a lathe and will be 40 inches tall John Lucas built one and it is pictured on his web page. thank you for any help/direction; I checked out the answered for cone shaped objects on your page but didn't find what I could use. thanks again. Henrywoodturner, parent teacher student . . . . . Answered by Harley Weston. 





A kennel for a beagle 
20130603 

From david: Hi, I'm building some beagle kennels and I am in need of help with an angle problem. I need to place a roof on my kennel with a drop of 2inches across 3ft 10inches. the posts on the right side will be 5ft and the post on the left will be 4ft 10in. the posts are 4x4 and the space to be covered is 3ft 10in from the outside of the 4x4. Please help, thanks. Answered by Penny Nom. 





Practical uses of trigonometry 
20121111 

From Michael: Where can I find books or information on real life function of sine and cosine? Answered by Penny Nom. 





A label to cover a plastic cup 
20121023 

From Kevin: I'm trying to make a label to cover the entire outer area or a plastic cup. I know there must be a way to figure out the dimensions needed, but I can't seem to figure it out. The circumference of the bottom of the cup is 21.4cm and the circumference at the top of the cup is 29.8cm. The cup is 14.5cm tall. What should the height of the arc from the plane connecting the two ends of the 21.4cm arc. I attached a diagram where x is the value I'm looking for. I'm guessing there is some simple relationship between the length of a line and the arc needed to turn that line into a perfect circle, but I don't know what it is. Can you figure this out and share it with me? Thanks.
Kevin Answered by Penny Nom. 





A tank with an inner walled compartment 
20121012 

From don: I have a tank 20 feet diameter, 19' 8" tall with an inner walled compartment that has a 7' 6" radius arc with in the tank. I need to figure out the volume of the inner area and the volume of the larger area. Answered by Harley Weston. 





Making a wind sock 
20120828 

From John: I am trying to build a wind sock and need to be able to lay the shape
out on cloth. I need the wind sock front opening (diameter) to be
3 1/2" and the rear opening diameter to be 1". The windsock needs
to be 9 1/2" long. I tried using the example of the person trying to
make a crayfish trap but got confused and could not figure out my
numbers. Any help would be greatly appreciated.
Thanks
John 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. 





Cutting a pipe at an arbitrary angle 
20091024 

From Carol: I have read your article on cutting pipe,etc. at a 45 degree angle. I need to develop
an equation and pattern for cutting any size pipe (3" to 7") to any degree. I don't
understand how to transfer the wave pattern to graph paper.
Thanks. Answered by Harley Weston. 





A barrel on its side 
20081113 

From Dave: Question from Dave:
How many gallons are left in a 36x60 in. barrel (laying on its side) and has 16 in. of gasoline left. I have attached a diagram. Answered by Harley Weston. 





Cutting a pipe at an arbitrary angle 
20080920 

From John: from the original question Al asked about cutting a 200 diameter pipe in 45 degrees. can someone explain the math steps required to creating the graph. I am trying to do the same thing only using a 150 degree cut. Answered by Harley Weston. 





Cutting a 200 diameter pipe at 45 degree angle 
20080410 

From Al: i want to cut a 200 diameter pipe in 45degrees. Can you demonstrate how to develop a flat rap around please Answered by Harley Weston. 





Where do you use trigonometry? 
20070821 

From jenny: where do you use trigonometry besides architecture and engineering? Answered by Stephen La Rocque. 





A perpendicular intersection of two barrel vaults 
20060721 

From Neal: I'm wanting to build a series of architectural models of different roman and medieval buildings out of cardboard. Once I have perfected the models I want to print them out on card stock so that school kids (or anyone else) can make the buildings.
A feature of many of these models is the cross or groin vault (a perpendicular intersection of two barrel vaults).
A single barrel vault is easy to imagine as a plane (a rectangular piece of cardboard) that will be folded into a semicircular arch.
The intersection of a second barrel vault and this one is presenting me with problems. The second plane needs to have an ellipse cut into it so that when it is folded into the arch, it will mate up with the curve of the first barrel vault.
Given that the two pieces of card have identical widths (and therefore identical arcs in cross section) is there a way to calculate the ellipse that needs to be cut so that it can be cut before the second arch is folded? Answered by Edward Doolittle. 

