Joining walls into a trianglular prism

Question

I'm helping to build a set for my son's theatre program, and am stumped by what is probably a simple trig problem (it's been a while).

We want to build a triangular prism of walls, so that we can rotate it and have 3 different sets. Each wall is 8'x8'x3.5" (built by conjoining two 4'x8'x3.5" flats into one). I want to join all three of these walls into an equilateral triangle, wherein the back corners of each wall touch. To do so, I need to build a triangular platform for the walls to screw onto. Obviously, the length of the sides of this platform needs to be longer than 8' to account for the thickness of the wall. How long does each side of this triangle need to be? I can't figure out what math I need to do to solve this problem, and would greatly appreciate any help.

Answer 1

Hint

We know:

• The length of the side $BC$
• The angle $\angle BAC = 30^{\circ}$, $\angle CBA = 90^{\circ}$

We have to compute:

• The length of side $AB$
• The length of the 'big side' $X=a+2|AB|$