A circle has a chord that goes from pi/3 to pi/8 radians on the circle. If the area of the circle is 48 pi , what is the length of the chord?

1 Answer
Douglas K.
Nov 5, 2016

The chord, c ~~ 4.45

Explanation:

Given the Area, A, of the circle is 48pi, allows us to solve for the radius, using the equation:

A = pir^2

48pi = pir^2

r^2 = 48

Two radii and the chord form a triangle with the angle, theta = pi/8 - pi/3, between the two radii. This allows us to use the Law of Cosines to find the length of the chord, c:

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

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

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

c^2 = 96(1 - cos(pi/8 - pi/3))

c = sqrt(96(1 - cos(pi/8 - pi/3)))

c ~~ 4.45

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