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If the angle of elevation of a balloon from two consecutive kilometre-stones along a road are 30° and 60° respectively, then the height of the balloon above the ground will be
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√3 km 2 -
1 km 2 -
2 km √3 - 3 √3 km
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Correct Option: A
AB = Height of balloon = h km
BD = x km, CD = 1 km
From ∆ ABD.
| tan 60° = | BD |
| ⇒ √3 = | x |
| ⇒ x = | km ......(i) | √3 |
From ∆ ABC,
| tan 30° = | BC |
| ⇒ | = | |||||
| √3 | + 1 | |||||
| √3 | ||||||
| ⇒ √3 h = | + 1 | √3 |
| ⇒ √3 h - | = 1 | √3 |
| ⇒ | = 1 | √3 |
⇒ 2h = √3
| ⇒ h = | km | 2 |
