A circle has a sector with area 27 pi and a central angle of 120 degrees. what’s the area of the circle?

Step-by-step explanation:

This may appear problem of geometry but can be simply solved using concept of ratio.

Since circle is uniform figure , hence area is uniformly distributed over the circle. Hence , area will be equally distributed for each angle of circle.

Given

sector with 120 degree angle has area

to get area covered by unit angle we divide both angle and area by 120

sector 120/120 degree angle has area

sector with 1 degree has area

We know that total angle for a circle is 360 degree.

Hence, area for circle will be 360 times multiplied the area of sector with 1 degree has area of same circle

Thus area of circle =

hope this !

step-by-step explanation:

d = distance between moon and sun, which in this problem is the hypotenuse of a right triangle.  

the distance y is the side opposite to angle x in the right triangle.   use the definition of the sine function from basic trigonometry.

sin(x) = y/d ⇒

d = y/sin(x)