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boat is heading towards a lighthouse, whose beacon-light is 126 feet above the water. From point AA, the boat’s crew measures the angle of elevation to the beacon, 12^{\circ}
∘
, before they draw closer. They measure the angle of elevation a second time from point BB at some later time to be 25^{\circ}
∘
. Find the distance from point AA to point BB. Round your answer to the nearest foot if necessary.

Respuesta :

The distance from point A to point B rounded to the nearest foot is; 887 ft

How to calculate the bearing?

The vertical change is 126 feet.

At point A, the angle is 6º, while the horizontal position is of a. Thus;

tan 6 = 126/a

a = 126/(tan 6)

a = 1198.8 ft

At point B, the angle is of 22º, while the horizontal position is b. Thus;

b = 126/tan 22

b = 311.9 ft

Thus;

Distance from point A to point B is;

a - b = 1198.8 - 311.9

⇒ 887 ft

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