Question

The lower window of a house is at height of $2m$ above the ground and its upper windowis $4m$ vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows windows are observed tom be ${60}^{\circ }$ and ${30}^{\circ }$, respectively. Find the height of the balloon above the ground.

Answer 1

$\tan 60°=\frac{4+h_1}{x}\Rightarrow \sqrt{3}=\frac{4+h_1}{x}\to 1$

$\tan 30°=\frac{h_1}{x}\Rightarrow \frac{1}{\sqrt{3}}=\frac{h_1}{x}\to 2$

Dividing equations $2/1$

$\frac{1}{\sqrt{3}\times \sqrt{3}}=\frac{h_1\times x}{x(4+h_1)}$

$\Rightarrow 3h_1=4+h_1$

$\Rightarrow 2h_1=4$

$h_1=2$

Height of balloon$=2+6=8m$