Question

The line of sight from a small boat to the light at the top of a 35-foot lighthouse built on a cliff 25 feet above the water makes a 35 degree angle with the water. To the nearest foot, how far is the boat from the cliff?

Answer 1

We can find the x by using TOA

`\begin{gathered} \text{tan 35=}\frac{opposite}{\text{adjacent}} \\ \tan 35=(60)/(x) \\ x\tan 35=60 \\ x=\frac{60}{\tan \text{ 35}} \\ x=(60)/(0.7002) \\ x=86\text{ foot} \end{gathered}`

The distance of the boat from the cliff is 86 foot