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

136 m

Step-by-step explanation:

The diagram illustrating this problem is attached below:

Using trigonometric ratio:

`\tan 32\degree=(85)/(x)`

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

`\begin{gathered} x\tan 32\degree=85 \\ (x\tan 32\degree)/(\tan 32\degree)=(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.