Question

A boat is 400 meters from the base of a cliff. Jackie, who is at the top of the cliff. notices that the angle of depression to the boat is 64" How high is the cliff?

Answer 1

Let's draw for a better understanding of the situation.

This way, it is possible to observe that we can use trigonometric ratios to find the height of the cliff.

In this case, we can use the tangent which is the ratio of the opposite and adjacent sides of a given angle. In the given situationn, the angle is 64° and the opposite and adjacend sides are the height "h" and 400 respectively.

Use this information to find how high is the cliff.

`\begin{gathered} \tan 64=(h)/(400) \\ 400\cdot\tan 64=h \\ 820.12=h \end{gathered}`

The cliff is 820.12m high.