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Two men standing on same side of a pillar 75 metre high, observe the angles of elevation of the top of the pillar to be 30° and 60° respectively. The distance between two men is :
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- 100 √3 metre
- 100 metre
- 50 √3 metre
- 25 √3 metre
Correct Option: C
AB = Height of pole = 75 metre
C and D ⇒ positions of persons
Let, BC = x metre, BD = y metre
∆ACB = 60°; ∆ADB = 30°
In ∆ABC,
| tan60° = | ||
| BC |
| ⇒ √3 = | ||
| x |
| ⇒ x = | = 25 √3 metre | |
| √3 |
In ∆ABD
| tan30° = | ||
| BD |
| ⇒ | = | ||
| √3 | y |
⇒ y = 75 √3 metre
∴ CD = y – x = (75 √3 - 25 √3) metre CD = 50√3 metre
