Question

How do you find the radius of each circle if the area of the sector is 28 and the angle is 150 degrees?

Answer 1

radius `~=4.625`

Explanation:

If a sector of `150^@` has an area of `28`

then a sector of `1^@` has an area of `28/150` = 0.186667#

and a full circle, which is a sector of `360^@` has an area of `0.186667xx360 = 67.200`

The area of a circle is `pir^2`

so `pir^2 = 67.200`
and
`color(white)("XXX")r^2 = 67.200/pi = 21.39042`

and
`color(white)("XXX")r = sqrt(21.39042) ~= 4.625`