-
A vertical pole and a vertical tower are standing on the same level ground. Height of the pole is 10 metres. From the top of the pole the angle of elevation of the top of the tower and angle of depression of the foot of the tower are 60° and 30° respectively. The height of the tower is
-
- 20 m
- 30 m
- 40 m
- 50 m
Correct Option: C
AB = Pole = 10 metre
CD = Tower = h metre (let)
∠ DAE = 60°
∠ EAC = ∠ ACB = 30°
From ∆ ABC,
| tan 30° = | BC |
| ⇒ | = | |||
| √3 | BC |
⇒ BC = 10 √3 metre
∴ AE = 10 √3 metre
From ∆ ADE
| tan 60° = | AE |
| ⇒ √3 = | 10√3 |
⇒ DE = 10 √3 × √3
= 30 metre
∴ CD = Heigth of tower
= CE + ED = 10 + 30
= 40 metre
