mathematics help: Challenging math problem… - Help.com

what are the actual numbers? (it’s makes things easier)

I need a generic solution, I need to be able to plug in values for R1, h, and w and get a result that is theta.

oh, wow. that is a tough one. I am an engineering student with a math minor and it would take me forever to solve that one.

I think I’ve got a way of solving this.

You can get the maximum height of the shape by adding h to the sin(theta)*R1:
h + sin(theta)*R1

You can find the width of where the top comes to a point (coming from the right) with w - cos(theta)*R1

Since theta is equal to the arctangent of the total height over the width from the top to the right corner:
arctan( (h + sin(theta)*R1) / (w - cos(theta)*R1) )

I don’t know if you need to simplify it any further, but I think that’s right. Good luck.

for simplicity: A= cos(theta), B = sin(theta), C = tan (theta) = B/A
You have:
W = RA + (h + RB)/C
W =RA + h/C + RB/C
W = RA +h/(B/A) +(RB)/(B/A)
W = RA +hA/B + + RA
W =2RA +hA/B
WB = 2RAB +hA
WB = A(2RB +hA)
(WB)^2 = [A(2RBg +hA)]^2n

After you square, you going to have sin^2 on the right side and bunch of sin and cos of different power. Use substitution : cos^2 = 1 - sin^2. You are going to end up with sin only. use another substitution sin(theta) = x. You will end up with the polynomial of the power 4. Solve for x and you are done.
I hope it helped