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From a point on a bridge across the river, the angles of depression of the banks on opposite sides of the river are 30° and 45° respectively. If the bridge is at a height of 2.5 m from the banks, then the width of the river is (Take √3 = 1.732)
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- 5.83 metre
- 6.83 metre
- 5.76 metre
- 6.87 metre
Correct Option: B
AD = Height of bridge = 2.5 metre
∠EAB = ∠ABD = 45°;
∠FAC = ∠ACD = 30°
In ∆ABD,
| tan 45° = | ⇒ 1 = | ⇒ CD = 2.5 metre | ||
| BD | BD |
In ∆ACD,
| tan 30° = | ⇒ | = | |||
| CD | √3 | CD |
⇒ CD 2.5√3 metre
CD = (2.5 × 1.732) metre = 4.33 metre
∴ BC = (2.5 + 4.33) metre = 6.83 metre
