Question

A length of an arc is 10π if the radius of the circle is 12, what is the measure ofthe arc intercepted by the sector?

Answer 1

We can find the measure of the arc intercepted by the sector by using the formula:

$S=r\theta$

where r is the radius, s is the length of the arc and theta is the angle

From the question, s = 10π and r=12

substitute and solve for theta

$10\pi=12\theta$

Divide both-side by 12

$\theta=\frac{10\pi}{12}=\frac{5\pi}{6}$

The angle is 5π/6 rad

We can convert to degree by multiplying the answer by 180/π

That is;

$\theta=\frac{5\pi}{6}\times\frac{180}{\pi}=150^o$