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.

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:

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