Question

determine the length of the on - ramp (in red) using the diagram shown.

Explanation:

Step1: Recall the arc - length formula

The formula for the length of an arc of a circle is \(s = r\theta\), where \(r\) is the radius of the circle and \(\theta\) is the central angle in radians.

Step2: Identify the radius and the central angle

From the diagram, the radius \(r = 80\) m. The central angle \(\theta=\frac{\pi}{3}\) radians.

Step3: Calculate the arc - length

Substitute \(r = 80\) and \(\theta=\frac{\pi}{3}\) into the formula \(s=r\theta\). Then \(s = 80\times\frac{\pi}{3}=\frac{80\pi}{3}\approx\frac{80\times3.14}{3}=\frac{251.2}{3}\approx83.73\) m.

Answer:

\(\frac{80\pi}{3}\text{ m}\approx83.73\text{ m}\)