Question

Find the central angle θ which forms a sector area 18 square feet of a circle of a radius of 10 feet?

Answer 1

The central angle has a measure of `0.36` radians or `20.626` degrees.

Explanation:

The area of a sector can be determined by the following formula.

`A=1/2r^2theta`

`r` is the radius. `theta` is the central angle measure.

In this problem, we want to solve for `theta`. We can rearrange the formula to make this easier.

`(2A)/r^2=theta`

Now, we just need to plug in the values we know for area and radius.

`(2(18))/10^2=theta`

`36/100=theta`

`0.36=theta`

It is important to remember that this answer is in radians. If we want the answer in degrees, we can convert it.

`"radians"="degrees"*pi/180`

`0.36="degrees"*pi/180`

`64.8/pi="degrees"`

`20.626="degrees"`