Question

Sam is framing a closet under a stairway. The stairway is 18 ft 5 in.​ long, and its angle of elevation is 38 degrees. Find the depth of the closet to the nearest inch?

Answer 1

`(18 times 12 + 5) \ cos 38^circ approx 174` in

Explanation:

This question illustrates how bad Trigonometry as taught really is.

I've never built a staircase, but I've watched someone do it on TV. They have their two essential measurements: rise and run. They use a carpentry square like this:

In the US we often use a 7 inch rise and an 11 inch run, a slope of `7/11.` We notch that from the stringers, typically 12 inch wide planks. We make successive right triangles where the carpentry square reads `11` on the long side and `7` on the short side similar to the figure. When constructing the stairs the treads are 11 inches wide and the risers are 7 inches minus the thickness of the tread.

Angle plays no role. An angle would turn these exact measurements into an approximation. It's totally unhelpful.