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Two towers A and B have lengths 45 m and 15 m respectively. The angle of elevation from the bottom of the tower B to the top of the tower A is 60°. If the angle of elevation from the bottom of tower A to the top of the tower B is θ then value of sin θ is :
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1 √2 -
1 2 -
√3 2 -
2 √3
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Correct Option: B
PQ = Tower A = 45 metre
RS = Tower B = 15 metre,
QS = x metre (let)
∠PSQ = 60° ; ∠RQS = θ
From ∆PQS,
| tanθ 60° = | |
| QS |
| ⇒ √3 = | ⇒ √3x = 45 | |
| QS |
| ⇒ x = | = 15√3 metre | |
| 5√3 |
From ∆RSQ,
| tanθ = | = | ||
| QS | 15√3 |
| ⇒ tanθ = | |
| √3 |
⇒ tanθ = tan 30°
⇒ θ = 30°
∴ sinθ = sin 30° = 1/2
