Question

Find the radian of an angle at the center of a ˚le with a radius of 65.0 cm that intercepts an arc length of 113 cm.

a. 0.836 radians
b. 1.738 radians
c. 1.725 radians
d. 0.642 radians

Answer 1

To find the radian measure of an angle that intercepts an arc length, divide the arc length by the radius. For an arc length of 113 cm and radius of 65.0 cm, the angle in radians is 1.738 radians.

Step-by-step explanation:

Finding the Radian Measure of an Angle

To find the radian measure of an angle at the center of a circle that intercepts an arc length, you can use the formula:

Angle in radians (θ) = Arc length (s) / Radius (r)

Given that the radius (r) is 65.0 cm and the arc length (s) is 113 cm, you can substitute these values into the formula:

θ = 113 cm / 65.0 cm

Upon calculation, you will get:

θ = 1.738 radians

Therefore, the correct answer is b. 1.738 radians.