Question

Find the length of the two missing sides of a right triangle given that one angle is 83.5​° and the length of the side adjacent to the angle is 13.7 centimeters.

Answer 1

opposite side: 120.24 cm

hypotenuse: 121.02 cm

Explanation:

The mnemoic SOH CAH TOA is useful here. It tells you ...

... Tan = Opposite/Adjacent

so

... Opposite = Adjacent×Tan = (13.7 cm)×tan(83.5°) ≈ 120.24 cm

It also tells you ...

... Cos = Adjacent/Hypotenuse

so

... Hypotenuse = Adjacent/Cos = (13.7 cm)/cos(83.5°) ≈ 121.02 cm