From the top of a lighthouse 200 feet high, the angle of depression of a boat is 22°. Find the distance from the boat to the foo
t of the lighthouse. The lighthouse was built at sea level.
2 answers:
Answer: The distance from the boat to the foot of the lighthouse is 495 feet
Step-by-step explanation: Please refer to the attached diagram. The angle of depression of the boat is 22°. That makes the point A to form an angle of 68° with the foot of the lighthouse, (point C). The boat is at point B, so the distance from the boat to the lighthouse is line CB (or a).
To calculate the distance we shall apply the trigonometrical ratio, since we already have a right angled triangle.
We have a reference angle A, an opposite side a, and an adjacent side 200.
Tan A = opposite/adjacent
Tan 68 = a/200
By cross multiplication we now have
Tan 68 x 200 = a
2.475 x 200 = a
495 = a
Therefore, the distance from the boat to the foot of the lighthouse is 495 feet.
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