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    Question

    Two buildings are 40 meters apart. The height of one

    building is 20 meters. From the top of the shorter building, the angle of elevation of the top of the taller building is 45°, and the angle of depression of its base is 30°. Find the height of the taller building.
    A 50 m Correct Answer Incorrect Answer
    B 55 m Correct Answer Incorrect Answer
    C 60 m Correct Answer Incorrect Answer
    D 65 m Correct Answer Incorrect Answer

    Solution

    Let the height of the taller building be H meters. The height difference between the two buildings is (H - 20) meters. From the angle of elevation: tan 45° = (H - 20) / 40   1 = (H - 20) / 40   H - 20 = 40   H = 60 m. Answer: c) 60 m

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