Question

A zip line is setup 150ft in the air, where a person can expect to zip line at a safe declining speed to the ground as they pass over a body of water, said to be 40 ft in length. Assuming that this cable were stretched tight, where the zip liner is approaching the ground at a 40∘ angle (not the top angle), how many feet of ground would be covered horizontally by the zip liner, not including the body of water? Round to the nearest foot

Answer 1

139 ft

Explanation:

So the zip line forms a right triangle. The height of the triangle is 150 ft, and the opposite angle is 40°. The horizontal distance covered by the zip liner can be found with trigonometry, specifically with tangent.

tan 40° = 150 / x

x = 150 / tan 40°

x ≈ 179 feet

But this includes the 40 ft long body of water, so the amount of ground covered is:

179 ft - 40 ft = 139 ft