A circle has a chord that goes from ( 5 pi)/8 to (4 pi) / 3 radians on the circle. If the area of the circle is 16 pi , what is the length of the chord?

1 Answer
Douglas K.
Aug 24, 2017

c ~~ 7.17

Explanation:

Use the formula

"Area" = pir^2

to find the value of r:

16pi = pir^2

r^2 = 16

r = 4

The angle between two radii to each end of the chord is:

theta = (4pi)/3-(5pi)/8

theta = (17pi)/24

Because the two radii and the chord form a triangle we can use The Isosceles case of The Law of Cosines to find the length of the chord, c:

c^2 = 2r^2(1-cos(theta))

c = sqrt(2(4)^2(1 - cos((17pi)/24)))

c ~~ 7.17

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