Question

A theater production group is making frames to support wall-like props. Three-foot beams form right triangles with 10-foot beams to allow them to stand, as shown in the image.

A right triangle is shown. The lengths of the 2 sides are 10 feet and 3 feet. The angle opposite to side with length 3 feet is x.

What is x, the angle at which the diagonal beam meets the 10-foot beam at the top of the frame?

16.7°
17.5°
72.5°
73.3°

Answer 1

The diagonal is the triangle's hypotenuse, so the side of length 3 is opposite angle x while the hypotenuse is √(10^2+3^2)=√109.
sin x = 3/√109 ≈ 0.2873, so x = arcsin(0.2873) ≈ 16.7°.

Answer: 16.7°.