The arc length of the arc which is intercepted by a central angle of 5π/6 radians is approximately 56.59 yd
We have full circumference subtending full angle on the center which is of 360 degrees.
[tex]2\pi^c = 360^\circ = \text{Full circumference}[/tex]
The superscript 'c' shows angle measured is in radians.
If radius of the circle is of r units, then:
[tex]1^c \: \rm covers \: \dfrac{circumference}{2\pi} = \dfrac{2\pi r}{2\pi} = r\\\\or\\\\\theta^c \: covers \:\:\: r \times \theta \: \rm \text{units of arc}[/tex]
For this case, the radius of the circle is [tex]r = 21\dfrac{5}{8} \: \rm yd = \dfrac{21 \times 8+5}{8} = \dfrac{178}{8} = 21.625\: yd[/tex]
The angle subtended by arc on the center is [tex]\theta = \dfrac{5\pi}{6} \approx \dfrac{5 \times 3.14}{6} \approx 2.6167 \: \rm radians[/tex]
Thus, the length of the arc is [tex]\theta \times r \: \rm yd[/tex] which is:
[tex]\theta \times r \approx 2.6167 \times 21.625 \approx 56.59 \: \rm yd[/tex]
Thus, the arc length of the arc which is intercepted by a central angle of 5π/6 radians is approximately 56.59 yd (rounded to 2 figures because π had two figures after 3)
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