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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 tanθ   can be expressed as tanθ=  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 tanθ = x y ⇒tan 30 ° = x y ⇒ 1 3 = x y ⇒y =x 3 Similarly,   
  tan 60 ° = x+4 y ⇒ 3 = x+4 x 3 ⇒3x =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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