Q1. [1]
A 30 m long rope is tightly stretched and tied from the top of pole to the ground. If the rope makes an angle of $60°$ with the ground, the height of the pole is :
- (a) $10\sqrt{3}$ m
- (b) $30\sqrt{3}$ m
- (c) $15$ m
- (d) $15\sqrt{3}$ m
Previously asked in CBSE board exam
2025 30/4/1 Q10
Generated by claude-sonnet-4-6 · 2026-06-15 10:36 · grounding rag
Model Answer
(d) $15\sqrt{3}$ m
Using $\sin 60° = \dfrac{\text{height}}{\text{hypotenuse}}$: height $= 30 \times \sin 60° = 30 \times \dfrac{\sqrt{3}}{2} = 15\sqrt{3}$ m.
Explanation
The rope is the hypotenuse (30 m) and makes 60° with the ground. The pole (opposite side) = hypotenuse × sin 60°. Students sometimes confuse sin and tan here — use sin because hypotenuse is known, not the base.
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