Question

A boat is heading towards a lighthouse, where Natalie is watching from a vertical distance of 140 feet above the water. Natalie measures an angle of depression to the boat at point AA to be 12^{\circ} ∘ . At some later time, Natalie takes another measurement and finds the angle of depression to the boat (now at point BB) to be 27^{\circ} ∘ . Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Answer 1

Explanation:

Using the slope concept, it is found that the distance from point A to point B is of 521 feet.

What is a slope?

The slope is given by the vertical change divided by the horizontal change.

It's also the tangent of the angle of depression.

In this problem, the vertical change is of 118 feet.

At point A, the angle is of 12º, while the horizontal position is of , hence:

At point B, the angle is of 74, while the horizontal position is of , hence:

The distance in feet is of:

Answer 2

Answer:384

Explanation: