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A straight tree breaks due to storm and the broken part bends so that the top of the tree touches the ground making an angle of 30° with the ground. The distance from the foot of the tree to the point, where the top touches the ground is 10 m. Find the total height of the tree?
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- 10 √3 metre
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10√3 metre 3 - 10 (√3 + 1) metre
- 10 (√3 - 1) metre
Correct Option: A
AB = Height of tree
BD = 10 metre
AC = CD = broken part of tree
∠CDB = 30°
In ∆BCD
| tan30° | BD |
| ⇒ | = | √3 | 10 |
| ⇒ BC = | metre | √3 |
| Again, sin 30° = | CD |
| ⇒ | = | 2 | √3 × CD |
| ⇒ CD = | = | metre | √3 | √3 |
∴ AB = BC + CD
| = | + | = | √3 | √3 | √3 |
= 10 √3 metre
