applilcations of trigonometry

A surveyor wants to find the height of the top of a hill. He observes that the angles of elevation of the top of the hill at points C and D, 300m apart, lying on the base of the hill and on the same side of the hill are 30° and 45° respectively What is the height of the hill.

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  1. Let AB be the height of the mountain, where A is at the top and B is on the line containing C and D

    let BD = x, and because of the 45° angle in the right-triangle ADB, AB = x

    then by Pythagoras AD = √2 x

    In triangle ACD , angle C 30, angle CDA = 135, leaving 15° for angle CAD

    by the sine law
    √2 x/sin30 = 300/sin15
    x = 300 sin30/(√2 sin15)
    = ...

    you do the button pushing , (I got appr 409.8)

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