Question

The angles of elevation of the top of a tower from the bottom and top of a building of height d are $\beta$ and $\alpha$ respectively. Find the height of the tower.

Answer 1

Given $\angle ABD=\beta ,\angle ECD=\alpha ,BC=d,AB=EC$

$AB=\frac{AD}{\tan \beta }$

$EC=\frac{ED}{\tan \alpha }=\frac{AD-d}{\tan \alpha }$

We know that $AB=EC$

$\frac{AD}{\tan \beta }=\frac{AD-d}{\tan \alpha }$

Height of the tower $AD=\frac{d\tan \beta }{\tan \beta -\tan \alpha }$