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maths --plse help me..

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The angle of elevation of the top of a tower as observed from a point on the ground is alpha and on moving a meters towards the tower, the angle of elevation is beta .prove that the height of the tower is a (tan alpha*tan beta)/(tan beta - tan alpha)

  • maths --plse help me.. -

    make a sketch, label the height as h
    distance from last position to the tower as x

    tan (alpha) = h/(x+a)
    h = (x+a)tan alpha

    in the same way
    h = xtan beta
    (x+a)tan alpha = xtan beta
    x tan alpha - xtan beta = - a tan alpha
    x(tan alpah - tan beta) = -a tan alpha
    x = -a tan alpha/(tan alpha - tan beta)
    x = a tan alpha /(tan beta - tan alpha)

    h = xtan beta
    = a tan alpha * tan beta/(tan beta - tan alpha)
    as requested

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