Question

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is 100 meters, sees the balloon at an angle of elevation of $30^{\circ }$. If the balloon rises further vertically to a point where the angle of elevation as seen by the observer is $45^{\circ }$, then twice its height (in meters) from the ground is $($ Take $\sqrt{3}=1.73)$

Answer 1

Answer: 173

Let $A$ be the observer, $P$ be the initial position of the balloon and it is at $Q$ when the angle of elevation is $45^{\circ }$
From triangle $ABP$ and triangle $ABQ$,
$\Rightarrow AB=50\sqrt{3}=BQ$
and $BP=50$
So, $BQ=50(\sqrt{3})=50\times 1.73$
$\Rightarrow BQ=86.5$ meters
$\Rightarrow 2BQ=173$ $\Rightarrow 2BQ=173$