A wire is attached from a point $A$ on the ground to the top of a pole $BC$, making an angle of elevation as…

Question

A wire is attached from a point $A$ on the ground to the top of a pole $BC$, making an angle of elevation as $60°$. If $AB = 5\sqrt{3}$ m, then length of the wire is

Accepted Answer

## Model Answer **(A) 10 m** In right △ABC, AB = 5√3 m (base), angle of elevation = 60°. cos 60° = AB/AC → 1/2 = 5√3/AC → AC = **10 m**. ## Explanation The wire is the hypotenuse (AC). Use cos 60° = adjacent/hypotenuse = AB/AC. Since cos 60° = 1/2, AC = 2 × 5√3 is wrong — note AB here is the horizontal distance, so AC = AB/cos60° = 5√3 ÷ (1/2) = 10 m. Always identify which side is the hypotenuse (the wire/rope) and which trig ratio links the given side and required side.

Mathematics — CBSE Class 10 board question