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    Question

    A sniper on the parapet of a 50 feet high building was

    aiming at a target. The angle of depression that his rifle made was 45 °. How far away from the building was his target?
    A 50/√3 feet Correct Answer Incorrect Answer
    B 25√3 feet Correct Answer Incorrect Answer
    C 50 feet Correct Answer Incorrect Answer
    D 50√3 feet Correct Answer Incorrect Answer

    Solution

    Let θ be the angle of depression of the point on the ground as seen from the top of a tower, here θ = 45° Let AC be the height of the tower, here AC = 50 feet. Let the distance of the point on the ground from the foot of the tower, AB = x feet. Here, tan θ = AC/AB ⇒ tan 45° = 50/x ⇒ 1 = 50/x ⇒ x = 50 feet

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