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The distance between two vertical poles is 60 m. The height of one of the poles is double the height of the other. The angle of elevation of the top of the poles from the middle point of the line segment joining their feet are complementary to each other. The height of the poles are :
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- 10 m and 20 m
- 20 m and 40 m
- 20.9 m and 41.8 m
- 15 √2 m and 30 √2 m
Correct Option: D
BE = DE = 30 metre
∠AEB = θ ∴ ∠CED = 90° – θ
From ∆ ABE,
| tan θ = | BE |
| ⇒ tan θ = | 30 |
⇒ h = 30 tan θ ................(i)
From ∆ CDE,
| tan (90° – θ) = | 30 |
| ⇒ cot θ = | ⇒ h = 15cotθ ....(ii) | 15 |
By multiplying both equations,
h2 = 30 × 15 × tan θ. cot θ
⇒ h2 = 30 × 15
[∵ tan θ . cot θ = 1]
⇒ h = 15 √2 metre = AB
⇒ 2h = 30 √2 metre = CD
