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(B) Let the height of the balloon from the ground be $H$.Let the horizontal distance from the house to the balloon be $x$.Height of the lower window $

Vedclass · Accepted Answer

$8$

Vedclass · Answer

(B) Let the height of the balloon from the ground be $H$.Let the horizontal distance from the house to the balloon be $x$.Height of the lower window $(w_2)$ from the ground is $2\, m$.Height of the upper window $(w_1)$ from the lower window is $4\, m$,so its height from the ground is $2 + 4 = 6\, m$.In the right-angled triangle formed by the lower window,the balloon,and the horizontal line at the level of the lower window:$	an 60^{\circ} = \frac{H - 2}{x} \Rightarrow \sqrt{3} = \frac{H - 2}{x} \Rightarrow x = \frac{H - 2}{\sqrt{3}} \quad \dots(i)$In the right-angled triangle formed by the upper window,the balloon,and the horizontal line at the level of the upper window:$	an 30^{\circ} = \frac{H - 6}{x} \Rightarrow \frac{1}{\sqrt{3}} = \frac{H - 6}{x} \Rightarrow x = \sqrt{3}(H - 6) \quad \dots(ii)$Equating $(i)$ and $(ii)$:$\frac{H - 2}{\sqrt{3}} = \sqrt{3}(H - 6)$$H - 2 = 3(H - 6)$$H - 2 = 3H - 18$$2H = 16$$H = 8\, m$.Thus,the height of the balloon above the ground is $8\, m$.

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