Question

A building is made by keeping the lower window of a building at a height of $2m$ above the ground and its upper window $6m$ vertically above the lower window in view to have proper sunlight. At certain instant, the angle elevation of a balloon from these windows are observed to be ${60}^o$ and ${30}^o$ respectively. Find the height of the balloon above the ground. What values are depicted, if the building owner in a view to use the proper sunlight by maintaining the level of height of window in the building?

Answer 1

A/C to question balloon Makes angle ${30}^{\circ }$ with the lower window

These in $\Delta ABC$

$tan30=\frac{AC}{BC}$

$\frac{1}{\sqrt{3}}=\frac{AC}{BC}=\frac{AE+EC}{BC}$

$BC=(AE+6)\sqrt{3}$

Now, similarly

Balloon makes ${60}^{\circ }$ with appear window

Thus in $\Delta ADE$

$tan60=\frac{AE}{DE}$

$\sqrt{3}=\frac{AE}{DE}$

Thus $=AE=\sqrt{3}DE$

also $DE=BC$

So, $AE=BC\sqrt{3}$

Thus $BC=(BC\sqrt{3}+6)\sqrt{3}$

$=3BC+6\sqrt{3}$

Thus $BC=3\sqrt{3}$

$AE=9$

So, height of the balloon from ground

$=9+6+2=17m$