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The upper part of a tree broken by the wind makes an angle of 30° with the ground and the distance from the root to the point where the top of the tree touches the ground is 10 m. What was the height of the tree?
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- 10√3
- 10/ √3
- 20 √3
- None of these
Correct Option: A
Let us draw the figure from the given question.
Let, QMP be the tree. When broken by the wind, its top P strikes the ground at A such that ∠QAM = 30°, AQ = 10m and MA = MP.
In figure QAM , we know that
| MQ | = | tan30° | ⇒ | MQ | = | 10 | m |
| AQ | √3 |
| and, | AM | = | sec30° | ⇒ | AM | = | 10 ( | 2 | ) = | 20 |
| AQ | √3 | √3 |
| ∴ Height of the tree = | QM + MP | = | QM + AM | = | 10 | + | 20 |
| √3 | √3 |
| Height of the tree = | 30 | = | 10 √3 [ Multiplying by √3 in numerator and denominator both ] |
| √3 |
Hence , Height of the tree = 10 √3 m
