Question

The angle of elevation of the top of a tower standing on a horizontal plane form point $A$ is ${\alpha }^o$. After walking a distance $d$ towards the foot of tower, angle is ${\beta }^o$, find height of tower

Answer 1

REF.image

$tan\beta =\frac{h}{x}$ $tan\alpha =\frac{h}{d+x}$

$\therefore x=\frac{h}{tan\beta }$

$\therefore tan\alpha =\frac{h}{d+\frac{h}{tan\beta }}$

$\therefore dtan\alpha +\frac{h.tan\alpha }{tan\beta }=h$

$\therefore h=\frac{dtan\alpha }{1-\frac{tan\alpha }{tan\beta }}=\frac{dtan.tan\beta }{tan\beta -tan\alpha .}$