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    Question

    From the top of a building, the angle of depression of

    two cars on a straight road are 30┬░ and 60┬░ respectively. If the height of the building is 120 meters, find the distance between the two cars.
    A 100тИЪ3 meters Correct Answer Incorrect Answer
    B 80тИЪ3 meters Correct Answer Incorrect Answer
    C 120тИЪ3 meters Correct Answer Incorrect Answer
    D 40тИЪ3 meters Correct Answer Incorrect Answer

    Solution

    Let the distance of the first car from the base of the building be x, and the distance of the second car be y. For the first car, using tan(30┬░) = height / distance: tan(30┬░) = 120 / x 1/тИЪ3 = 120 / x x = 120тИЪ3 meters. For the second car, using tan(60┬░) = height / distance: tan(60┬░) = 120 / y тИЪ3 = 120 / y y = 120 / тИЪ3 = 40тИЪ3 meters. The distance between the two cars is x - y: 120тИЪ3 - 40тИЪ3 = 80тИЪ3 meters. Correct answer: b

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