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A man standing on the bank of a river observes that the angle of elevation of the top of a tree just on the opposite bank is 60°. But angle of elevation is 30° from a point which is at a distance 20 √3 ft away from the bank. Then the height of the tree is :
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- 60 ft
- 45 ft
- 30 ft
- 15 ft
Correct Option: C
Suppose, height of tree = AB = h foot
BC = width of river = x foot
CD = 20 3 foot
∠ACB = 60° and ∠ADB = 30°
In ∆ABC,
| tan60° = | BC |
| ⇒ √3 = | x |
⇒ h = √3x foot ...............(i)
In ∆ABD,
| tan30° = | BD |
| = | = | |||
| √3 | x + 20√3 |
⇒ √3h x = + 20 √3
| ⇒ √3h = | + 20√3 | √3 |
⇒ 3h = h + 20 √3 × √3
⇒ 2h = 60
| ⇒ h = | = 30 feet | 2 |
