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The angle of elevation of the top of a tower from a point A on the ground is 30°. On moving a distance of 20 metres towards the foot of the tower to a point B, the angle of elevation increases to 60°. The height of the tower is
  • a)
    √3 m
  • b)
    5√3 m
  • c)
    10√3 m
  • d)
    20√3 m
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The angle of elevation of the top of a tower from a point A on the gro...

Given, AB = 20 m
Let, the height of the tower = h metre
And, BC = x metre
∴ AC = AB + BC = (20 + x) m
In ΔACD,

h = (h √3 – 20) √3 [From eq. (i)]
h = 3h – 20 √3
2h = 20 √3
h = 10 √3
∴ The height of the tower is 10 √3 meter.
Hence, option C is correct.
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