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trigo

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Points A and B are on the same horizontal line from the foot of a hill and the angles of depression of these points from the top of the hill are 30deg and 22deg, respectively. If the distance between A and B is 75m, what is the height of the hill?

  • trigo -

    The 2 lines of sight represent the
    hypotenuse of 2 rt. triangles, and
    the height of the hill represents the vertical side of both triangles. The
    hor. side of smaller triangle(d) is
    measured from the bottom of hill to A.
    The hor. side of the larger triangle
    is = to d + 75m.

    Tan30 = h/d, h = d * Tan30.
    h = (d+ 75)* Tan22

  • trigo -

    The 2 lines of sight represent the
    hypotenuse of 2 rt. triangles, and
    the height of the hill represents the vertical side of both triangles. The
    hor. side of smaller triangle(d) is
    measured from the bottom of hill to A.
    The hor. side of the larger triangle
    is = to d + 75m.

    Tan30 = h/d,
    h = d * Tan30.
    h = (d + 75)* Tan22
    Substitute d * Tan30 for h.
    d * Tan30 = (d + 75) * Tan22.
    Solve for d:
    0.5774d = (0.4040d + 30.30.
    0.5774d - 0.4040d = 30.30
    0.1774d = 30.30.
    d = 30.30/0.1774 = 174.74m.
    h = 174.74 * Tan30 = 100.9m = height
    of hill.

  • trigo -

    27

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