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A straight highway leads to the top of the base of a 50 meter tall tower. Frm the top of the tower, if yhe angles of depression of two cars on the road are 30° and 60° , then the distence between the tow cars is ................meter.

  • science -

    We form 2 rt. triangles with a common ver. side:
    Y = 50 m. = Ver. side.
    X1 = hor. side of larger triangle(30 Deg).
    X2 = hor. side of smaller triangle(60 Deg).

    tan30 = Y/x1 = 50/X1.
    X1 = 50/tan30 = 86.6 m.

    X2 = 50/tan60 = 28.9 m.

    d = X1 - X2 = 86.6 - 28.9 = 57.7 m. =
    The distance between cars.

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