In a circle of radius $10\text{cm}$, a chord subtends a central angle of $80^{\circ }$. Find the length of the chord. Give your answer correct to two decimal places.

Step-by-step solution

1. Use the chord length formula $l=2r\sin \left(\frac{\theta }{2}\right)$.
2. Here $r=10\text{cm}$ and $\theta =80^{\circ }$, so $\frac{\theta }{2}=40^{\circ }$.
3. Calculate $\sin 40^{\circ }\approx 0.6428$.
4. Substitute: $l=2\times 10\times 0.6428=12.856\text{cm}$.
5. Round to two decimal places: $l=12.86\text{cm}$.

Concept tested: chord length

Published 25 August 2026 · How this solution was prepared and checked

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