Question

From a window 10 m above the ground level the tangent of angle of elevation of the top of a tower is $\frac{5}{2}$ and tangent of depression of the foot of the lower is $\frac{1}{4}$. Find the height of the lower.

Answer 1

Let CE be the height of the tower. Let the angle of elevation of the top of the tower be $\alpha$ and the angle of depression of the foot of the lower be $\beta$.

$tan\alpha =\frac{5}{2}$ and $tan\beta =\frac{1}{4}$ (given)

In $\Delta BDC$

$tan\beta =\frac{10}{x}$

$\frac{1}{4}=\frac{10}{x}$

$\therefore x=40m$

In $\Delta BDE$

$tan\alpha =\frac{h}{x}$

$\frac{5}{2}=\frac{h}{40}$

$h=100m$

$\therefore$ height of tower $=h+10=100+10=110m$