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math help pls

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Two observers who are 5 km apart simultaneously sight a small airplane flying between them. One observer measures a 51.0-degree inclination angle, while the other observer measures a 40.5-degree inclination angle. At what altitude is the
airplane flying?

  • math help pls -

    Draw a triangle ABC , A and B the position of the observers and C the position of the plane.
    Drop an altitude from C to AB, call it CD.
    Label angle A as 51 and angle B as 40.5 degrees
    Label AD as x, then DB = 5-x

    In triangle ACD, cot51 = x/h
    x = hcot51
    In triangle DBC cot 40.5 = (5-x)/h
    5-x = hcot40.5 or
    x = 5 - hcot40.5

    then hcot51 = 5-hcot40.5
    hcot51 + hcot40.5 = 5
    h = 5/(cot51 + cot40.5)
    = .....

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