Question

If the arc length of a sector in the unit circle is 4.2, what is the measure of the angle of the sector?

Answer 1

The unit circle is a circle with radius $r=1$, so you have

$L=r\theta\implies4.2=\theta$

where $\theta$ is measured in radians, so $\theta\approx241^\circ$.

Answer 2

Answer:  4.2 radian or  $241^{\circ}$

Step-by-step explanation:

Let $\theta$ represents the measure of the angle of the sector.

We know that in a unit circle , the radius = 1 unit

The formula to calculate the length of arc of sector is given by :-

$L=r\theta$

Then , the measure of the angle of the sector is given by :-

$\theta=\dfrac{L}{r}\\\\\Rightarrow\ \theta=\dfrac{4.2}{1}=4.2\text{ radian}$

In degrees , the measure of the angle of the sector will be :-

$4.2\times\dfrac{180^{\circ}}{\pi}=240.642273955\approx241^{\circ}$