A circle has a chord that goes from $\frac{5 π}{3}$ $( 5 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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A circle has a chord that goes from $\frac{5 π}{3}$ $( 5 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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Answer 1 · 2016-05-10T12:53:14

$\Rightarrow chord length \approx 3.977$ $=> "chord length "~~3.977$ to 3 decimal places

Explanation:

The angle of the arc is $∣ ∣ ∣ (\frac{17}{12} - \frac{5}{3}) π ∣ ∣ ∣ = ∣ ∣ ∣ - \frac{1}{4} π ∣ ∣ ∣ = \frac{1}{4} π$ $|(17/12-5/3)pi|=|-1/4 pi| = 1/4 pi$

$π \equiv 180^{o}; \frac{1}{2} π \equiv 90^{o}; \frac{1}{4} π \equiv 45^{o}$ $pi-=180^o; 1/2pi-=90^o; 1/4pi-= 45^o$

Let the radius be $r$ $r$

Tony B
$To determine the radius$ $color(blue)("To determine the radius")$

Known: area $= π r^{2}$ $=pi r^2$

$\Rightarrow 27 π = π r^{2}$ $=>27pi=pi r^2$

Divide both sides by $π$ $pi$

$\Rightarrow 27 = r^{2}$ $=>27=r^2$

$\Rightarrow r = \sqrt{27} = \sqrt{3 \times 9} = \sqrt{3 \times 3^{3}}$ $=>r=sqrt(27) =sqrt(3xx9)=sqrt(3xx3^3)$

$r = 3 \sqrt{3}$ $r=3sqrt(3)$

Thus the chord length $= 2 \times 3 \sqrt{3} \times cos (\frac{3}{8} π)$ $= 2xx3sqrt(3)xxcos(3/8 pi)$

$\Rightarrow r \approx 3.977$ $=> r~~3.977$ to 3 decimal places

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A circle has a chord that goes from $\frac{5 π}{3}$ $( 5 pi)/3$ to $\frac{17 π}{12}$ $(17 pi) / 12$ radians on the circle. If the area of the circle is $27 π$ $27 pi$ , what is the length of the chord?

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A circle has a chord that goes from ( 5 pi)/3 5π3( 5 pi)/3 to (17 pi) / 12 17π12(17 pi) / 12 radians on the circle. If the area of the circle is 27 pi 27π27 pi , what is the length of the chord?

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