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The angles of elevation of the top of a temple, from the foot and the top of a building 30 m high, are 60° and 30° respectively. Then, the height of the temple is
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- 50 metre
- 43 metre
- 40 metre
- 45 metre
Correct Option: D
AB = Height of building = 30 metre
CD = Height of temple = h metre
AB = CE = 30 metre
∴ DE = (h – 30) metre;
BC = AE = x metre
∠DAE = 30°; ∠DBC = 60°
In ∆BCD,
| tan 60° = | ⇒ √3 = | BC | x |
⇒ h = √3 x metre ..... (i)
In ∆ADE,
| tan 30° = | AE |
| ⇒ | = | √3 | x |
⇒ x = √3 h – 30 √3 ..... (ii)
∴ h = √3 x
= 3h – 30 × 3
⇒ 3h – h = 90 ⇒ 2h = 90
| ⇒ h = | = 45 metre | 2 |
