Question

The lower window of a house is at $2m$ above the ground and its upper window is $4m$ vertically above the lower window. At certain instant the angle of elevation of balloon from these windows are observed to be ${60}^0$ and ${30}^0$ respectively. Then the height of the balloon above ground is

• A. $12m$
• B. $14m$
• C. $8m$
• D. $16m$

Answer 1

The correct option is C $8m$

Let the height of the first window be $EG=2m$

and, the height of the second window be $CG=(2+4)m=6m$

Let, $AB$ be $x$ and $FG$ be $y$

From $\Delta ABC$

$⟹\tan 30°=\frac{AB}{BC}$

$⟹\frac{1}{\sqrt{3}}=\frac{x}{y}$

$⟹y=\sqrt{3}x$

From $\Delta ADE$

$⟹\tan 60°=\frac{AD}{DE}$

$⟹\sqrt{3}=\frac{x+4}{y}$

$⟹\sqrt{3}y=x+4$

$⟹\sqrt{3}\times \sqrt{3}x=x+4$

$⟹3x=x+4$

$⟹2x=4$

$⟹x=2$

Hence, the height of the balloon from the ground is$=(2+4+2)m=8m$