Trigonometry

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A passenger in an airplane flying at an altitude of 10 kilometers sees two towns directly to the left of the plane. The angles of depression to the towns are 28° and 55°. How far apart are the towns?

  • Trigonometry -

    tan55o = Y/X1 = = 10km/X1
    X1 = 1okm/tan55 = 7 km.

    tan28o = Y/(x1+x2) = 10km/(x1+x2).
    x1+x2 = 10km/tan28 = 18.8 km.
    7+X2 = 18.8
    X2 = 11.8 km.

    d = 18.8 - 7 = 11.8 km = Distance bet.
    the two towns.

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