th circle below has the center o and a radius of lenght 5. if the area of the shaded reigon is 20 pie, what is the value of x.

a: 18

b: 36

c: 45

d: 54

e: 72

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Posts: 1761

Posts: 1761

i also need an explanation

"i prefer toaster studels... my icing is like artwork for fat kids"-Rainbow*Stylin

Posts: 1241

that's tough..what class is this? trigenometry?

yeah.

Posts: 754

B

quality posts not quantity!

Posts: 502

A (18)

If the shaded region's area is 20pi, the area of the non-shaded region is 5pi (total area 25pi - pi*r^2). That means the angle besides x and the right angle (we'll call it y) is 1/5 of 360 degrees, or 72 degrees (because the area of the non-shaded region is 1/5 the total area). Since x, y, and right angle must add up to 180 degrees (because it's a triangle) x must be 180 - (72+90), or 18.

If the shaded region's area is 20pi, the area of the non-shaded region is 5pi (total area 25pi - pi*r^2). That means the angle besides x and the right angle (we'll call it y) is 1/5 of 360 degrees, or 72 degrees (because the area of the non-shaded region is 1/5 the total area). Since x, y, and right angle must add up to 180 degrees (because it's a triangle) x must be 180 - (72+90), or 18.

Posts: 4

Well the area of a circle is (pie)(r)(r).

Area of the total circle = (pie)(5)(5) = 25(pie)

If you think of the circle as 5 equal wedges, then one wedge ( which is what the triangle represents) is equal to 360/5 degrees which is = to 72 degrees.

Now that you know the angle of the lower left angle of the triangle, you can find the angle at x. 360-72-90 = 18 degrees.

So your answer is: a: 18.

Posts: 4

damn beat me to it.

Posts: 1761

hey guys thanks so much ++++ k. you saved my life hahaha

"i prefer toaster studels... my icing is like artwork for fat kids"-Rainbow*Stylin

Posts: 1014

i think you meant 180 - 72 - 90 = 18

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