Question

You are standing at the top of the Charleston Lighthouse. While looking out, you look down at an angle of depression of 27 degrees and see a boat. If the lighthouse is 140 feet tall, what is the horizontal distance between the boat and the bottom of the light house? Round your answer to the nearest tenth.

Answer 1

274.8 feet

Step-by-step explanation:

The diagram illustrating this problem is attached below:

The distance between the boat and the bottom of the lighthouse = x

Using trigonometric ratio:

`\tan 27\degree=(140)/(x)`

Cross multiply:

`x\tan 27\degree=140`

Divide both sides by tan 27.

`\begin{gathered} (x\tan 27\degree)/(\tan 27\degree)=(140)/(\tan 27\degree) \\ x=274.77 \\ x\approx274.8ft \end{gathered}`

The horizontal distance between the boat and the bottom of the light house is 274.8 feet (correct to the nearest tenth)