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The shadow of a vertical tower increases 10 metre, when the altitude of the sun changes from 45° to 30°. What is the height of tower ? (π = 1.73)
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- 12.65 metre
- 13.65 metre
- 14.65 metre
- 16.65 metre
- 12.65 metre
Correct Option: B
AB = Tower = h Metre
CD = 10 metre, AC = x metre
(let)
∠BCA = 45°, ∠BDA = 30°
In ∆ACB,
| tan 45° = | ||
| AC |
| ⇒ 1 = | ||
| x |
⇒ h = x --- (i)
In ∆DAB,
| tan 30° = | ||
| AD |
| ⇒ | = | |||
| √x + 10 | 7 |
⇒ x + 10 = √3h
⇒ h + 10 = √3h
⇒ h (√3 – 1) = 10
| ⇒ h = | ||
| √3 – 1 |
| = | × | |||
| √3 – 1 | √3 + 1 |
| = | = 5(1.73 + 1) | |
| 2 |
= 13.65 metre
