Posted by **Meenakshi** on Thursday, December 13, 2012 at 12:22pm.

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.. -
**Reiny**, Thursday, December 13, 2012 at 12:44pm
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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