Question

A boat is heading towards a lighthouse, where Dalvin is watching from a vertical distance of 138 feet above the water. Dalvin measures an angle of depression to the boat at point A. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

The given information is:

- Dalvin is watching from a vertical distance of 138 ft above the water.

- He measures an angle of depression to the boat at point A to be 13°.

- At some later time, he takes another measurement and finds an angle of depression of 45° at point B.

We need to find the distance from point A to point B.

A diagram of the problem is:

We can observe two right triangles. We can apply the trigonometric functions to find the adjacent sides of both triangles:

`\begin{gathered} \tan13=(138)/(A) \\ A=(138)/(\tan13) \\ A=597.7ft \\ \tan45=(138)/(B) \\ B=(138)/(\tan45) \\ B=138ft \end{gathered}`

Now we can find the distance from A to B, by subtracting B from A:

`Distance=A-B=597.7-138=459.7ft`

The answer is 459.7 ft.