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 foot of the lig

Question

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 foot of the lighthouse. The lighthouse was built at sea level.

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Ximena 2 weeks 2021-09-12T03:40:51+00:00 2 Answers 0

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    0
    2021-09-12T03:41:55+00:00

    Answer:

    495 feet

    Step-by-step explanation:

    tan22° = 200/d

    so, d = 200/tan22°

    Then, d = 495.0173707 => 495 feet to the nearest foot

    :)>

    0
    2021-09-12T03:42:49+00:00

    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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