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Q.

The lower window of a house is at a height of 2 m 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 to be $60 °$ and $30 °$ respectively. Find the height of the balloon above the ground.

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a

2 m

b

4 m

c

6 m

d

8 m

answer is D.

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Detailed Solution

Given that the lower window of a house is at a height of 2 m above the ground and its upper window is 4 m vertically above the lower window.
We have to find the height of the balloon above the ground.
The value for the trigonometric identities can be evaluated by using the right-angled triangle the value for

tan θ

can be expressed as

tan θ = opposite adjacent

Suppose window 1 be 2m above the ground and window 2 be 4m above the window 1.
Then, by using the figure geometry,
Question Image

Question Image

tan θ = x y ⇒ tan 30 ° = x y ⇒ 13 = x y ⇒ y = x 3 Similarly,

tan 60 ° = x + 4 y ⇒ 3 = x + 4 x 3 ⇒ 3 x = x + 4 ⇒ x = 2

Thus, the height of the balloon from the ground is,

⇒ h = 2 + 4 + 2 ∴ h = 8 m

The height of the balloon above the ground is 8m.
Therefore, the correct option is 4.

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