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trigonometry

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An aeroplane at an altitude of 200m observes the angles of depression of opposite points on the two banks of a river to be 45 degree and 60 degree. Find in metres, the width of river.

  • trigonometry -

    Let H be the altitude (which you already know), and D be the horizontal distance from the plane to the nearest bank of the river. Let w be the width of the river.

    H/D = tan 60
    H/(D + w) = tan 45

    Not that the second equation implies that
    H = D + w
    and the first equation implies that
    H = sqrt3 * D

    Solve for w in terms of H, using substitution to eliminate D.

    H = H/sqrt3 + w

    H(1 - 1/sqrt3) = w

  • trigonometry -

    Shut up

  • trigonometry -

    Right answer

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