A circle has a chord that goes from #pi/4 # to #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 · 2018-04-18T06:14:54

#color(purple)("Length of Chord " d = 2r sin theta ~~ 5.3 " units"##

Given #" Area = 48 pi, theta = pi / 4 - pi/ 8 = pi / 8#

![http://www.engineeringexpert.net/Engineering-Expert-Witness-Blog/determining-chord-length-on-circle-earth]( useruploads.socratic.org )

#"Chord length " d = 2r * sin theta#

Given #"Area of circle " = pi r^2 = 48pi#

#r = sqrt46 = 4 sqrt3#

#"Length of Chord " d = 2r * sin theta = 2 * 4 sqrt 3 * sin (pi / 8)#

#color(purple)(d = 8 sqrt 3 sin (pi/8) ~~ 5.3 " units"# #