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The angle of elevation of the top of a building from the top and bottom of a tree are x and y respectively. If the height of the tree is h metre, then (in metre) the height of the building is
  • a)
  • b)
  • c)
  • d)
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
The angle of elevation of the top of a building from the top and botto...

Given, the height of the tree, CD = h metre
Let, the height of the building, AB = H metre
And, BC = a metre
∴ AE = AB – EB = (H – h) metre [∵ CD = BE]
In ΔABC,

a = H cot y ...(i)
Now, in ΔADE,

a = (H – h) cot x ...(ii)
From equations (i) and (ii),
H cot y = (H – h) cot x = H cot x – h cot x
H(cot x – cot y) = h cot x

∴ The height of the building

Hence, option C is correct.
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