Find The Height of The Aeroplane Above The Ground

From an aeroplane above a straight  road the angles of depression of two positions at a distance 20 m apart on the road are observed to be 30 degree and 45 degree. The height of the aeroplane above the ground is :

  1. 10√3 m
  2. 10(√3 -1 ) m
  3. 10 (√3 +1) m
  4. 20 m
Manish Listener Asked on 24th July 2015 in Maths.
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1 Answer(s)

Answer: (3) 10 (√3 +1) m
Explanation:-
Let be the height of the plane = h m
In the figure-

Tan30o = h/X + 201/sqrt.3 = h/(X + 20)
X + 20 = h sqrt.3
X = h sqrt.3 – 20          …………….. (1)

Tan45o = h/X
1 = h/X
X = h    ………………………………………. (2)
Comparing equation (1) & (2)
h = h sqrt.3 – 20
h – h sqrt.3 = – 20
h (sqrt.3 – 1) = 20
h = 20/(sqrt.3 – 1)
= 20 (sqrt.3 + 1)/(sqrt.3 – 1) (sqrt.3 + 1)
= 20 (sqrt.3 + 1)/(sqrt.3)2 – 12
= 20 (sqrt.3 + 1)/3 – 1
= 20 (sqrt.3 + 1)/2
= 10 (sqrt.3 + 1) m
Hence, the answer is (3) 10 (sqrt.3 + 1) m.

Anurag Mishra Professor Answered on 24th July 2015.
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