Question

Form a balloon vertical above a straight road, the angles of depression of two cars at an instant are found to be ${30}^o$ and ${60}^o$. If the cars are $100m$ apart, then what can be the maximum height of the balloon.

• A. $50(3+\sqrt{3})m$
• B. $150m$
• C. $100(3+\sqrt{3})m$
• D. $50\sqrt{3}m$
• E. $Noneofthese$

Answer 1

The correct option is D $50\sqrt{3}m$

Let $C$ and $D$ be the two cars

$A$ be the balloon

Given $CD=100m$

Angle of depression of two cars are ${30}^{\circ },{60}^{\circ }$

In $△ABC,\tan {60}^{\circ }=\frac{h}{BC}⟹BC=\frac{h}{\sqrt{3}}$

In $△ABD,\tan {30}^{\circ }=\frac{h}{BD}⟹BD=\sqrt{3}h$

$CD=BD-BC=\sqrt{3}h-\frac{h}{\sqrt{3}}=100$

$⟹\frac{(3-1)h}{\sqrt{3}}=100$

$⟹h=50\sqrt{3}m$

Height of the balloon is $50\sqrt{3}m$