A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{π}{8}$ $pi/8$ 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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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{π}{8}$ $pi/8$ 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 · 2018-04-18T06:14:54

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

Explanation:

Given $A r e a = 48 π, θ = \frac{π}{4} - \frac{π}{8} = \frac{π}{8}$ $" Area = 48 pi, theta = pi / 4 - pi/ 8 = pi / 8$

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

$Chord length d = 2 r \cdot sin θ$ $"Chord length " d = 2r * sin theta$

Given $Area of circle = π r^{2} = 48 π$ $"Area of circle " = pi r^2 = 48pi$

$r = \sqrt{46} = 4 \sqrt{3}$ $r = sqrt46 = 4 sqrt3$

$Length of Chord d = 2 r \cdot sin θ = 2 \cdot 4 \sqrt{3} \cdot sin (\frac{π}{8})$ $"Length of Chord " d = 2r * sin theta = 2 * 4 sqrt 3 * sin (pi / 8)$

$d = 8 \sqrt{3} sin (\frac{π}{8}) \approx 5.3 units$ $color(purple)(d = 8 sqrt 3 sin (pi/8) ~~ 5.3 " units"$ #

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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{π}{8}$ $pi/8$ 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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Explanation:

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A circle has a chord that goes from π4pi/4 to π8pi/8 radians on the circle. If the area of the circle is 48π48 pi , what is the length of the chord?

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A circle has a chord that goes from $\frac{π}{4}$ $pi/4$ to $\frac{π}{8}$ $pi/8$ radians on the circle. If the area of the circle is $48 π$ $48 pi$ , what is the length of the chord?