Final answer:
To find the arc length of a circle that subtends a 60° angle with a radius of 42 cm, the formula (Central Angle / 360°) × Circumference is used. The circumference is first calculated using C = 2πr, yielding a length of 504 cm, from which the arc length is derived to be 84 cm.
Step-by-step explanation:
To calculate the length of the arc that subtends an angle of 60° at the center of the circle with a radius of 42 cm, we shall use the formula relating the arc length, radius, and central angle in degrees. The circumference C of a circle is given by C = 2πr, and the arc length formula for a circle is:
Arc length (As) = (Central Angle / 360°) × Circumference of the Circle
Here, our central angle (Θ) is 60°, and the radius (r) is 42 cm. Using the provided value of π as 22/7, the circumference of the circle is C = 2 × (22/7) × 42 cm.
We can calculate the circumference of the circle as follows:
C = 2 × (22/7) × 42 = 2 × 6 × 42 = 2 × 252 = 504 cm
Now, we can find the arc length using the formula:
As = (60°/360°) × 504 cm = (1/6) × 504 cm = 84 cm
Therefore, the arc length is 84 cm.