A circle has a chord that goes from #( pi)/2 # to #(15 pi) / 8 # radians on the circle. If the area of the circle is #48 pi #, what is the length of the chord?

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Answer 1 · 2018-04-18T10:06:25

#color(green)("Chord Length " d ~~ 12.8#

#"Given : " delta = (15pi)/8 - pi / 2 = (11pi) / 8 #

#"Area of the circle " A = pi R^2 = 48 pi#

#R = (sqrt 48 *cancel pi ) /cancel pi = sqrt 48 = 4 sqrt3#

#"Chord Length " d = 2 * R sin delta = 2 * 4 sqrt3 * sin ((11pi)/8)#

#d = 8 sqrt 3 * sin ((11pi) / 8) ~~ 12.8#