A circle has a chord that goes from $\frac{π}{3}$ $( pi)/3$ 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 · 2016-07-17T21:07:50

$8 \sqrt{3} sin (\frac{37}{48} π) \approx 9.14$ $8sqrt(3)sin(37/48 pi) ~~9.14$ to 2 decimal places

Area of a circle is $π r^{2}$ $pir^2$
$\Rightarrow π r^{2} = 48 π$ $=> pir^2=48pi$

$\Rightarrow r^{2} = 48$ $=> r^2=48$

$\Rightarrow r = \sqrt{2^{2} \times 2^{2} \times 3}$ $=>r=sqrt(2^2xx2^2xx3)$

$\Rightarrow r = 4 \sqrt{3}$ $=>r=4sqrt(3)$
'~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

The angle of the arc is
$\frac{15 π}{8} - \frac{π}{3} = π (\frac{45 - 8}{24}) = \frac{37}{24} π$ $(15pi)/8-pi/3" " =" " pi((45-8)/24)" "=" "37/24 pi$

So 1/2 of this angle is $\frac{37}{48} π$ $37/48pi$

Tony B

The length of the chord is: $2 (r sin (\frac{37}{48} π))$ $2(rsin(37/48 pi))$

$= 8 \sqrt{3} sin (\frac{37}{48} π) \approx 9.14$ $=8sqrt(3)sin(37/48 pi) ~~9.14$ to 2 decimal places

A circle has a chord that goes from ( pi)/3 π3( pi)/3 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?