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If the angle of elevation of the sun changes from 45° to 60°, then the length of the shadow of a pillar decreases by 10 m. The height of the pillar is :
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- 5 (3 - √3) metre
- 5 (√3 + 1) metre
- 15 √3 + 1 metre
- 5 (3 + √3) metre
Correct Option: D
AB = Height of pillar = h metre (let)
CD = 10 metre
∠ACB = 45°
∠ADB = 60°
BD = x metre (let)
From ∆ABC
| tan 45° = | BC |
| ⇒ 1 = | x + 10 |
⇒ h = (x + 10) metre (i)
From ∆ABD
| tan 60° = | BD |
| ⇒ √3 = | x |
| ⇒ x = | metre (ii) | √3 |
From equation (i),
| h = | + 10 | √3 |
| ⇒ h - | = 10 | √3 |
| ⇒ | = 10 | √3 |
⇒ h(√3 - 1) = 10√3
| ⇒ h = | √3- 1 |
| = | (√3- 1)(√3+ 1) |
| = | 3 - 1 |
= 5√3 (√3 + 1)
= 5 (3 + √3)metre
