Answer:
See Explanation
Step-by-step explanation:
The question is incomplete, as the sector, its area and the angle at the center are not given.
I will solve this using the following illusration
The area of a sector is:
[tex]Area= \frac{\theta}{360} * \pi r^2[/tex]
Assume that:
[tex]\theta = 120[/tex]
[tex]Area = 20[/tex]
The equation becomes
[tex]20= \frac{120}{360} * \pi r^2[/tex]
Simplify
[tex]20= \frac{1}{3} * \pi r^2[/tex]
Take: [tex]\pi = 3.14[/tex]
[tex]20= \frac{1}{3} *3.14* r^2[/tex]
Cross Multiply
[tex]3.14 * r^2 = 20 * 3\\[/tex]
Solve for [tex]r^2[/tex]
[tex]r^2 = \frac{20 * 3}{3.14}[/tex]
[tex]r^2 = 19.11[/tex]
Take square roots
[tex]r = \sqrt{19.11[/tex]
[tex]r = 4.4[/tex]
The radius of the sector of a circle whose area is 20 square units and angle subtends at the center of 120° is 4.4 units.
It is a locus of a point drawn equidistant from the center. The distance from the center to the circumference is called the radius of the circle.
The angle subtends at the center is 120 degrees.
The area of the circle is 20 units.
We know that the area of a circle is given as
[tex]\rm Area = \dfrac{\theta }{360} \pi r^2[/tex]
Then we have the radius of the sector will be
[tex]\rm r = \sqrt{\dfrac{360*20}{120*\pi}}\\\\\\r = 4.37 \approx 4.4[/tex]
The radius of the sector is 4.4 units.
More about the circle link is given below.
https://brainly.com/question/11833983
