Question

An arc is 6.5 cm long and it subtends a central angle of 45°. Find the radius of the circle.

Circles
ANSWERED
asked 2021-06-19

An arc is 6.5 cm long and it subtends a central angle of \(45^{\circ}\). Find the radius of the circle.

Expert Answers (1)

2021-06-20

Use the arc length formula: \(L=2\pi r\times(\frac{\theta}{360^{\circ}})\)

where r is the radius and \(\theta\) is the central angle

Subtitute \(L=6.5 cm\) and \(\theta=45^{\circ}\) then solve for r:

\(6.5=2\pi r\times(\frac{45^{\circ}}{360^{\circ}})\)

\(6.5=(\frac{\pi}{4})r\)

Multiply both sides by \(\frac{4}{\pi}:\)

\(6.5\times(\frac{4}{\pi})=r\)

\(r \sim 8.3 cm\)

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