Question

find the length of the arc on a circle of radius r intercepted by a central angle θ. round answer to two decimal places. 6) r = 11.41 inches, θ = 60° solve the problem.

Explanation:

Step1: Convert angle to radians

First, convert the central angle \(\theta = 60^\circ\) to radians. We know that \(180^\circ=\pi\) radians, so \(60^\circ=\frac{60}{180}\pi=\frac{\pi}{3}\) radians.

Step2: Use arc length formula

The formula for the length of an arc \(s\) of a circle with radius \(r\) and central angle \(\theta\) (in radians) is \(s = r\theta\). Here, \(r = 11.41\) inches and \(\theta=\frac{\pi}{3}\) radians. So we substitute these values into the formula: \(s=11.41\times\frac{\pi}{3}\).

Step3: Calculate the value

Now, calculate \(11.41\times\frac{\pi}{3}\approx11.41\times1.0472\approx11.95\) (rounded to two decimal places).

Answer:

The length of the arc is approximately \(\boldsymbol{11.95}\) inches.