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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 in metres is
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- √3
- 5 √3
- 10 √3
- 20 √3
Correct Option: C
Let, AB = height of tower = h metre
∠ ACB = 30°,
∠ADB = 60°
CD = 20 metre ; BC = x metre
In ∆ ABC,
| tan30° = | BC |
| ⇒ | = | √3 | x |
⇒ x = √3 h .... (i)
In ∆ ABD,
| tan60° = | BD |
| ⇒ √3 = | x - 20 |
⇒ h = √3 x – 20 √3
= √3 √3 h – 20 √3
⇒ h = 3h – 20 √3
⇒ 3h – h = 20 √3
⇒ 2h = 20 √3
| ⇒ h = | = 10√3 metre | 2 |
