Question

In the diagram below what is the length of arc AC ? Round to the nearest inch.

Answer 1

22inches

Explanation:

Length of an arc is expressed as

theta/360° × 2πr where:

theta is the angle subtended by the arc

r is the radius of the circle

The angle substended by the arc will be <CBA = 180°-75° = 105°

radius of the circle is BA = 24inches/2

Radius = 12inches

Length of the arc AC = 105°/360°×2π(12)

= 105°/360° × 24π

= 7/24 × 24π

= 7π

= 7 × 3.142

= 21.99 approximately 22inches

Answer 2

As AB is a diameter, then m∠CBA=180^{0}-75^{0}=105^{0}.
∠CBA is a central angle, so its measure multiplied by radius is the length of arc AC.
Note that
`105^(0)=7\cdot 15^0` and
`15^(0)= (\pi)/(12)`. Then
`105^(0)= (7\pi)/(12) = (7\cdot 3.14)/(12)=1.83` and length of the arc is
`12\cdot 1.83=21,96`.The correct answer is 22 in.