A balloon is rising vertically upwards. At an instant, an observer...

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}^{\text{o}} .

If the balloon rises further vertically to a point where the angle of elevation as seen by the observer is

{45}^{\text{o}}

, then its height (in meters) from the ground is
(Take

\sqrt{3} = 1.73

)

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is

Correct answer

36.5

Step-by-step solution

A balloon is rising vertically upwards. At an instant, an observer on the ground, whose distance from the balloon is
Let $A$ be the observer, $P$ be the initial position of the balloon and it is at $Q$ when the angle of elevation is ${45}^{\text{o}}$

From triangle $ABP$ and triangle $ABQ$ ,
$⇒ AB = 50\sqrt{3} = BQ$
and $BP = 50$
So, $PQ = BQ - BP = 50\left(\sqrt{3} - 1\right)$

$= 50\left(0 . 73\right) = 36 . 5$ meters

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