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The angle of elevation of the top of a building and the top of the chimney on the roof of the building from a point on the ground are x and 45° respectively. The height of building is h metre. Then the height of the chimney, (in metre) is :
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- h cot x + h
- h cot x – h
- h tan x – h
- h tan x + h
Correct Option: B
AB = Buidling = h metre
AD = Chimney = y metre
From ∆BCD,
| tan45° = | BC |
| ⇒ 1 = | BC |
⇒ BC = h + y ..... ... (i)
From ∆ABC,
| tan x = | BC |
| ⇒ tan x = | BC |
⇒ BC = h cot x ...........(ii)
From equations (i) and (ii),
h + y = h cot x
⇒ y = (h cot x – h) metre
