Math question

[Craig D Peltier]

See my rough sketch. I have 2 cat boxes to build and a bench in the middle of this bay window.
Angle is 22.5 degrees. How can I figure out the length of my front , back, top, sides etc.
The dimensions are from back 52.5 wide an its 14" wide x 18 tall.

Whats the easiest way to do this. I do have sketchup but havent learned it yet.
I have a program thats the grandmother of actrix and if I draw a box an then from corner take a line it says the angle but its for example like this 225.14 etc. Im looking for 22.5 right?

I guess I could take a sliding rule and use the 22.5 angle off of that and do a template but there must be an easier program to do this on.

Please help...

Sheet diagram.pdf

[Brian Kerley]

Well, I guess I'm not too sure what lengths you need. It'd be fairly easy to do using some trig . Could you append your sketch to show what dimensions you are wanting to know and I'd be more than happy to help you out.

[Eddie Darby]

If you want to avoid using math, then make a cut-out with an old cardboard box and some tape, until it looks right to your eye, and then get your measurements.

[Craig D Peltier]

Well, I guess I'm not too sure what lengths you need. It'd be fairly easy to do using some trig . Could you append your sketch to show what dimensions you are wanting to know and I'd be more than happy to help you out.

Heres another pdf.

Cat box.pdf

Thanks

[Tom Veatch]

Heres another pdf.

Thanks

Assuming the included angle in the top right corner is 67.5 degrees (complement of 22.5 degrees), the length of the right side is 14/sin(67.5) = 15.153. The length of the bottom side is 52.5 - 14/tan(67.5) = 46.701.

If the assumed angle is different, just plug the correct angle into the formula in place of the 67.5 value.

[Tom Henderson2]

HI Craig-

Sorry to work you so hard on this, but you really need to indicate what the angle is on your sketch. I know you mentioned 22.5 degrees in your initial post, but it isn't clear if that is the angle that the bay window makes with the walls, or the acute angle in the second sketch, or what.

The devil is in the details....

-Tom H.

[Brian Kerley]

Ok, here's the way to do it. I'm assuming that the interior angle at the top right is 67.5 degrees. So, with a length of 14" on the opposite side, that would give you a total hypotenuse length of:

opposite / (sin angle) = hypoteneuse
14/sin 67.5 = 15.153 inches (make sure your calculator is in radians, not degrees)

Then, the other long side will be the following
52.5 - adj = ??

So, the adjacent side of the right triangle is going to be:
opposite / (tan angle) = adjacent
14/tan 67.5 = 5.799 inches

So, the other side is 52.5-5.799 = 46.701 inches

That gives you the right edge a length of 15 5/32 inches and a bottom edge a length of 46 45/64 inches.

What I would do is not worry about it though. Cut a piece of wood with dimensions of 52.5" x 14". Then, on one corner, draw your angle from one side to the other, and cut it off. Then it will be pretty accurate without having to bust out the magnifying glass on your ruler.

[Craig D Peltier]

HI Craig-

Sorry to work you so hard on this, but you really need to indicate what the angle is on your sketch. I know you mentioned 22.5 degrees in your initial post, but it isn't clear if that is the angle that the bay window makes with the walls, or the acute angle in the second sketch, or what.

The devil is in the details....

-Tom H.

Its a 22.5 degree angle that I want the box end built at. Its the angle of the bay window. So essentailly if I pull all three units away from wall one inch the angle still remains the same I believe.

[David DeCristoforo]

MATH??? What math? Draw it out full size. Forget the math!

[Alex Yeilding]

opposite / (sin angle) = hypoteneuse
14/sin 67.5 = 15.153 inches (make sure your calculator is in radians, not degrees)

I think you said that backwards. If you want the sine of 67.5 degrees, you need the calculator set to degrees, not radians.

[Brian Kerley]

Yeah, sorry, meant degrees not radians. Ever tell yourself not to screw something up and you end up doing it regardless?

[Greg Cuetara]

MATH??? What math? Draw it out full size. Forget the math!

I Kinda like David's math!

[Gary Muto]

Too many unknowns for me. I would need at least one more length or one angle, assuming the other two are 90 degrees.
edit. since I started to reply and delayed my response I see the angle is 22.5 degrees.

[Stephen Edwards]

MATH??? What math? Draw it out full size. Forget the math!

That's my style, too! Forget the math. Just build it to fit and look nice!

[Mike Conley]

Here is what it looks like when I draw it in AutoCAD.