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The height of a tower is 100 m. When the angle of elevation of the sun changes from 30° to 45°, the shadow of the tower becomes P meter smaller. The value of P is :
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- 100 m
- 100 √3 m
- 100( √3 - 1) m
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100 m √3
Correct Option: C
As per given figure , we have
Let, AB be the tower and AC and AD be its shadows.
Then, AB = 100 m.
In triangle BDA ,
| AD | = | cot45° = 1 | ⇒ | AD | = 1 |
| AB | 100 |
⇒ AD = 100 m.
And In triangle BCA ,
| AC | = | cot30° = √3 | ⇒ | AC | = √3 |
| AB | 100 |
⇒ AC = 100 √3 m.
∴ P = AC - AD = 100(√3 - 1) m.
Hence ,The value of P is 100(√3 - 1) m.
