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Q.

The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45 °  . If the angle of elevation of the top of a flagstaff fixed at the top of the tower, from A is 60 °  , then find the height of the flagstaff.

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a

120( 3 −1)m  

b

121( 3 −1)m  

c

122( 3 −1)m  

d

123( 3 −1)m   

answer is A.

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Detailed Solution

Given that the angle of elevation of the top of a tower at a distance of 120m from a point A on the ground is 45. The angle of elevation of the top of a flagstaff fixed at the top of the tower, from A is 60.
We have to find the height of the flagstaff.
The angle of elevation of the top of a tower at a distance of 120 m from a point A on the ground is 45^(@). If the angle of elevation of the In a right-angle triangle,tanθ=  Opposite side   Hypotenuse  .  
Let the height of flagstaff be h m and that of the tower be x m.
As △ABD  is right angled, we get,
tan 45 o =1 ⇒ x AB =1 ⇒x=AB=120m  
As △ACD  is right angled, we get,
h+x 120 =tan 60 o = 3 ⇒h+x=120 3 ⇒h=120 3 −120 ⇒h=120 3 −1  
Therefore, the required height is 120( 3 −1)m  .
Therefore, the correct option is 1.
 
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