A triangle prism has a surface area of 350 square feet, a length of 15 feet, a height of 10 feet, and a of side of 5 feet. Find the width of the triangular prism.

One vertical face is 150 ft^2.

Another vertical faces is 50 ft^2.

That leaves 10W for a third vertical face,

in addition to which, one has the two triangular bases.

If the bases were right triangles,

their width would be sqrt (15^2-10^2) = sqrt (125)

= 5 sqrt (5) = about 11.7 ft,

but this doesn't "work" because the area of the two bases

would be 58.5 ft^2 and 117 ft^2 for the 3rd vertical face,

for a total surface area of about 375 ft^2.

Hence, the angle between the "side" and the "width" is larger than 90 degrees.

However, I'm assigning the name "theta" to the angle between "side" and "length".