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.

opposite side: 120.24 cm

hypotenuse: 121.02 cm

Step-by-step 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