Question

1. a sector has a central angle with a measure of 60° and an arc length of 10 cm. 5a find the radius of the sector, correct to two decimal places. radius = enter your next step here cm

Explanation:

Step1: Recall arc length formula

Arc length $l = r\theta$ (θ in radians). Convert $60^\circ$ to radians: $60^\circ \times \frac{\pi}{180^\circ} = \frac{\pi}{3}$.

Step2: Solve for radius r

Rearrange formula: $r = \frac{l}{\theta}$. Substitute $l=10$ cm, $\theta=\frac{\pi}{3}$: $r = \frac{10}{\pi/3} = \frac{30}{\pi}$.

Step3: Calculate numerical value

$\frac{30}{\pi} \approx 9.5492965855$. Round to two decimal places: 9.55.

Answer:

9.55