Question

find the length of the arc subtended by an 80° central angle and a radius of 34 m. round to the nearest tenth.

Explanation:

Step1: Convert degree to radian

The formula for arc length is \(s = r\theta\), where \(r\) is the radius and \(\theta\) is the central angle in radians.
To convert \(80^{\circ}\) to radians: \(\theta=80\times\frac{\pi}{180}=\frac{4\pi}{9}\) radians.

Step2: Calculate arc length

Given \(r = 34\) m and \(\theta=\frac{4\pi}{9}\), then \(s=r\theta=34\times\frac{4\pi}{9}\).

$$s=\frac{136\pi}{9}\approx\frac{136\times3.14159}{9}\approx\frac{427.256}{9}\approx47.5$$

Answer:

\(47.5\) m