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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 Fr - Mathematics

Answer in Brief

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 600 and 30respectively. Find the height of the balloon above the ground.

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Solution

Let the window G be 2 m above the ground. 
Window A be 4 m above the window G.
Balloon be at point B above the ground.
In ∆ABC,  

`tan 30°= h/x` 

`⇒ 1/sqrt3=h/x` 

`⇒ x= h sqrt3`       ................(1) 

In ∆BGD, 

`tan 60°=(BD)/(GD)`  

`⇒ sqrt3=( h+4)/x`

`⇒ x=( h+4)/sqrt3`  ................(2) 

From (i) and (ii) we get, 

`h sqrt3=( h+4)/sqrt3`

`⇒ 3h = h+4` 

`⇒2h=4`

`⇒h=2`

Hence, the height of the ballon above the ground = 2 + 4 + 2 = 8 m

  Is there an error in this question or solution?
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APPEARS IN

RD Sharma Class 10 Maths
Chapter 12 Trigonometry
Exercise 12.5 | Q 72 | Page 35
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