Question

You go ziplining with your family. There are two platforms, different in height, and you ride on a cable from one to the next. You are waiting to go from the taller platform to the lower platform. Horizontally, the platforms are 258 feet apart. The zipline is 450 feet long. Using the inverse of sine, what is the approximate angle of depression you will travel as you ride the zipline?(1

Answer 1

Let the vertical drop be h. Then h = sqrt(450^2 − 258^2) = sqrt(202500 − 66564) ≈ 368.7 ft.

sin(θ) = opposite/hypotenuse = 368.7/450 ≈ 0.8193, so
θ = arcsin(0.8193) ≈ 55.0°.

The angle of depression is about 55°.