Question

Find the length of the arc on a circle with a radius of 7 meters intercepted by a central angle with a measure of 80 degrees.

a) 560 meters
b) 11.4 meters
c) 2 meters
d) 9.8 meters

Answer 1

To calculate the arc length of a circle with a radius of 7 meters and a central angle of 80 degrees, the angle is first converted to radians and then multiplied by the radius using the arc length formula s = rθ, resulting in an arc length of approximately 9.8 meters.

Step-by-step explanation:

The question asks us to find the length of the arc on a circle with a radius of 7 meters intercepted by a central angle of 80 degrees. To solve this, we use the formula for arc length s, which is a portion of the circumference, given by s = r θ, where r is the radius and θ is the central angle in radians. Since there are 2π radians in 360 degrees, we must first convert the angle from degrees to radians.

Step 1: Convert the central angle to radians.
θ = (80 degrees)(π/180 degrees) = 4π/9 radians

Step 2: Calculate the arc length using the formula.
s = rθ = 7 meters * (4π/9 radians) = (28π/9) meters ≈ 9.8 meters

Therefore, the length of the arc is approximately 9.8 meters, which matches option d).