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

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Answer 1 · 2018-04-18T10:06:25

$Chord Length d \approx 12.8$ $color(green)("Chord Length " d ~~ 12.8$

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$Given : δ = \frac{15 π}{8} - \frac{π}{2} = \frac{11 π}{8}$ $"Given : " delta = (15pi)/8 - pi / 2 = (11pi) / 8$

$Area of the circle A = π R^{2} = 48 π$ $"Area of the circle " A = pi R^2 = 48 pi$

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

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

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

A circle has a chord that goes from ( pi)/2 π2( pi)/2 to (15 pi) / 8 15π8(15 pi) / 8 radians on the circle. If the area of the circle is 48 pi 48π48 pi , what is the length of the chord?