Question

A balloon is moving up in air vertically above a point $A$ on the ground. When it is at a height $h_1$, a girl standing at a distance $d$ (point $B$) from $A$ (see figure) sees it at an angle $45°$ with respect to the vertical. When the balloon climbs up a further height $h_2$, it is seen at an angle $60°$ with respect to the vertical. If the girl moves further by a distanœ $2.464d$ (point $C$). Then the height $h_2$ is (given $\tan 30°=0.5774)$:

• A. $1.464d$
• B. $0.732d$
• C. $0.464d$
• D. $d$

Answer 1

The correct option is D $d$

From figure trigonometry,
$\frac{h_1}{d}=\tan 45°$
$\therefore h_1=d$

And,
$\frac{h_1+h_2}{d+2.464d}=\tan 30°$
$\Rightarrow (h_1+h_2)\times \sqrt{3}=3.46d$
$\Rightarrow (h_1+h_2)=\frac{3.46d}{\sqrt{3}}\Rightarrow d+h_2=\frac{3.46d}{\sqrt{3}}=2d$
$\therefore h_2=d$