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A circle has a chord that goes from #( pi)/3 # to #(7 pi) / 8 # radians on the circle. If the area of the circle is #16 pi #, what is the length of the chord?

Answer 1

Autumn Armstrong

#color(crimson)("Length of the chord " bar(AB) ~~ 6.0147#

#"Area of circle " = A_c = 16 pi#

#"Radius " = bar (OA) = r = sqrt ((16 pi) / (pi)) = 4#

#"Given ' hat (AOB) = (7pi) / 8 - pi / 3 = (13pi ) / 24#

To fin #bar(AB)#

#"In "Delta AOM, (AM) = (AO) * sin (AOM)#

#bar (AB) = 2 * bar (AM)#

#:. bar (AB) = bar (AO) * (2 * sin (AOM) )#

#color(crimson)(bar(AB) = 4 * 2 * sin ((13pi)/48) = 6.0147#

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Answer 2

Savannah Aguilar

The length of the chord is ( \frac{15}{8} ) units.

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Answer from HIX Tutor

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