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Two men on the same side of a tall building notice the angle of elevation to the top of the building to be 30o and 60o respectively. If the height of the building is known to be h =120 m, find the distance (in meters) between the two men.

  • trig -

    Assuming that both observers are at an elevation level with the base of the building.
    Height of the building, H = 120m
    Distance of observer 1 = D1
    Angle of elevation = α
    By the definition of tangent = opp/adj
    H/D1=tan(α), therefore
    D1=H/tan(α)
    Since H and α are known, D1 can be calculated numerically.

    Distance of observer 2 = D2
    Angle of elevation = β
    H/D2=tan(β)
    D2=H/tan(β)

    Distance between observers = D2-D1

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