Question

A boat is heading towards a lighthouse, where Jeriel is watching from a vertical distance of 113 feet above the water. Jeriel measures an angle of depression to the boat at point AA to be 8degrees

∘
. At some later time, Jeriel takes another measurement and finds the angle of depression to the boat (now at point BB) to be 52degrees
∘
. Find the distance from point AA to point BB. Round your answer to the nearest tenth of a foot if necessary.

Answer 1

715.8 feet

Explanation:

You want the distance from point A to point B when the angles of depression to these points are 8° and 52°, respectively, from a height of 113 feet.

Tangent

The tangent ratio is related to an angle in a right triangle by ...

Tan = Opposite/Adjacent

In the geometry of this problem, the side adjacent to the relevant angle is the height of the lighthouse, 113 feet. The side opposite the angle is the distance from the lighthouse to the boat. The angle is the complement of the angle of depression.

Then the difference of the distances between the boats is ...

A -B = 113·tan(90°-8°) -113·tan(90°-52°) = 804.04 -88.29 ≈ 715.8 . . . feet

The distance from point A to point B is about 715.8 feet.

<95141404393>