Question

A right triangle has one side that measures 4 in. The angle opposite that side measures 80o.

What is the length of the hypotenuse of the triangle? Round to the nearest tenth.

3.9 in.
4.1 in.
22.7 in.
23.0 in.

Answer 1

Let the hypotenuse be h. Since the side 4 is opposite the 80° angle,
sin(80°) = opposite/hypotenuse = 4/h,
so h = 4 / sin(80°) ≈ 4 / 0.9848 ≈ 4.1 in.

Answer: 4.1 in.