maths plse help me..
posted by Meenakshi on .
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)

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