Question

2.) matt is standing on top of a cliff 305 feet above a lake. The measurement of the angle of depression to a boat on the lake is 42 degrees
. How far is the boat from the base of the cliff?

Answer 1

The boat is 338.7 feet away from the base of the cliff.

EXPLANATION

Let $d$ be the distance of the boat from the base of the cliff.

We can use alternate angles property to bring the angle of depression into the triangle.

Since the known side is opposite the $42\degree$ angle and the sede we are finding is adjacent to it, we use the tangent ratio.

From the diagram,

$\tan42\degree =\frac{305}{d}$

$d =\frac{305}{\tan42\degree}$

$d =\frac{305}{\0.900}$

$d =338.7$

Hence the boat is 338.7 feet away from the base of the cliff.