Guy wire to a 20 m pole: A 20 m vertical electric pole is anchored to the ground by a wire attached to its top. If the wire makes a 60° angle with the horizontal ground, find the length of the wire.
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A40/ √3 m
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B40 √3 m
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C20/ √3 m
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D20 √3 m
Answer
Correct Answer: 40/ √3 m
Explanation
Introduction / Context:The wire forms the hypotenuse of a right triangle with the ground (adjacent) and the pole (opposite). The angle given is with the horizontal, so use sine to relate opposite and hypotenuse.
Given Data / Assumptions:
- Pole height = 20 m.
- Angle with ground = 60°.
Concept / Approach:sin θ = opposite / hypotenuse → hypotenuse = opposite / sin θ.
Step-by-Step Solution:
Wire length L = 20 / sin 60° = 20 / (√3/2) = 40/√3 m.Verification / Alternative check:Numeric: √3 ≈ 1.732 → L ≈ 23.094 m; geometry consistent with a steep wire.
Why Other Options Are Wrong:40√3 is too long (would imply sin 60° < 0.5); 20√3 and 20/√3 arise from mixing cosine or tangent incorrectly.
Common Pitfalls:Using cos instead of sin since angle is with ground; rationalizing incorrectly; forgetting the 1/2 factor in sin 60°.
Final Answer:40/ √3 m