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=(10\pi)/(12)=(5\pi)/(6)`

The angle is 5π/6 rad

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

That is;

`\theta=(5\pi)/(6)*(180)/(\pi)=150^o`