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The lower window of a house is at height of 2m above the ground and its upper window is 4 m vertically above the lower window. At certain instant the angles of elevation of a balloon from these windows are observed tom be 60∘ and 30∘, respectively. Find the height of the balloon above the ground.

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6 m

7 m

8 m

5 m

answer is C.

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Detailed Solution

Given,
A house is height =2m Its upper window= 4 m Ground to upper window total height=2+4
Ground to upper window total height =6
Windows are observed tom be 60∘ and 30∘.
In triangle FCB, we have,

\tan 60^{\circ} = \frac{4 + h_{1}}{x}

\Rightarrow \sqrt{3} = \frac{4 + h_{1}}{x}

…………(1)
In triangle BDE, we have,

\tan 30^{\circ} = \frac{h_{1}}{x}

\Rightarrow \frac{1}{\sqrt{3}} = \frac{h_{1}}{x}

…………..(2)
Dividing the equation (2) by (1)

\frac{1}{\sqrt{3} \times \sqrt{3}} = \frac{h_{1} \times x}{x (4 + h_{1})}

\Rightarrow 3 h_{1} = 4 + h_{1}

\Rightarrow 2 h_{1} = 4

\Rightarrow h_{1} = 2

The height of balloon=

h_{1} +

Ground to upper window total height

= 2 + 6

= 8 m

Hence, the height of balloon is =8 m.
Option 3 is correct.

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