Question

At a point on ground level, the angle of elevation of a cliff is found to be such that its tangent is $\frac{5}{7}$. On walking $150$m away from the cliff, the tangent of new angle elevation is found to be $\frac{1}{2}$. Find the height of the cliff?

Answer 1

Height of cliff $=h$

$\tan {\theta }_2=\frac{5}{7}$

$\frac{h}{OB}=\frac{5}{7}$

$\Rightarrow 7h=5$ OB

$\tan {\theta }_1=\frac{h}{OA}=\frac{1}{2}$

$\Rightarrow 2h=OA$

$\Rightarrow 2h=OB+150$

$\Rightarrow 2h=\frac{7h}{5}+150$

$\Rightarrow \frac{3h}{5}=150$

$\Rightarrow h=250m$