A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{5 π}{8}$ $(5 pi) / 8$ radians on the circle. If the area of the circle is $120 π$ $120 pi$ , what is the length of the chord?

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Answer 1 · 2016-10-05T16:47:56

The length of the chord is: $c \approx 12.17$ $c ~~ 12.17$

We are given the area of the circle:

$A = pir² = 120pi$

$r = sqrt120$

Because two radii and the chord form a triangle, we can use the law of cosines to find the length of the chord:

$c² = a² + b² - 2(a)(b)cos(C)$

where $a = b = r = sqrt120$ , and $C = 5pi/8 - pi/4 = 3pi/8$

$c² = (sqrt120)² + (sqrt120)² - 2(sqrt120)(sqrt120)cos(3pi/8)$

$c ~~ 12.17$

A circle has a chord that goes from pi/4 π4pi/4 to (5 pi) / 8 5π8(5 pi) / 8 radians on the circle. If the area of the circle is 120 pi 120π120 pi , what is the length of the chord?