A circle has a chord that goes from #( 5 pi)/8 # to #(4 pi) / 3 # radians on the circle. If the area of the circle is #27 pi #, what is the length of the chord?

Question

1213 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2018-01-01T14:46:39

The length of a chord is # 9.32# unit.

Formula for the length of a chord is #L_c= 2r sin (theta/2)#

Where #r# is the radius of the circle and #theta# is the angle

subtended at the center by the chord. Area of circle is

# cancelpi * r^2 = 27 cancelpi :. r^2 = 27 or r = sqrt27 =3 sqrt3#

#theta= (4pi)/3-(5pi)/8 = (32pi-15pi)/24=(17pi)/24#

# :. L_c= 2 *3sqrt3 *sin (((17pi)/24)/2)# or

#L_c= 6sqrt3 * sin ((17pi)/48) = 6 sqrt3 * sin 63.75#

# ((17pi)/48)=63.75^0 # or

#L_c= 9.32# unit. The length of a chord is # 9.32# unit.[Ans]