Question

From the roof of an 85 meter cliff, Tim spots a hiker down below at an angle of depression of 32°. To the closest meter, how far is the hiker from the base of the cliff? (A quick answer is appreciated)

Answer 1

Answer:

136 m

Explanation:

The diagram illustrating this problem is attached below:

Using trigonometric ratio:

$\tan 32\degree=\frac{85}{x}$

We solve for x, the distance between the hiker and the cliff's base.

$\begin{gathered} x\tan 32\degree=85 \\ \frac{x\tan 32\degree}{\tan 32\degree}=\frac{85}{\tan 32\degree} \\ x=136.03m \\ x\approx136m \end{gathered}$

To the nearest meter, the distance between the hiker and the cliff's base is 136m.