Chapter 12.2, Problem 10CYU

To determine

Calculate the length of the arc of the path.

Answer to Problem 10CYU

The length of the arc of the path is $6.98feet$ .

Explanation of Solution

Given:

It is given in the question that the radius of the arc’s circle is $4feet$ and the angle of rotation of a tennis player is ${100}^{\circ }$ .

Concept Used:

In this, use the concept of changing the degree into radian by multiplying $\frac{\pi }{180}$ and the formula for the length of the arc is $s=r\cdot \theta$ .

Calculation: Since in a circle with radius r and central angle $\theta$ (in radians), the arc length s equals the product of r and $\theta$ .

Let’s find the measure of the center angle in radians:

  ${100}^{\circ }={100}^{\circ }\times \frac{\pi }{180}=\frac{5\pi }{9}radian$

Now, use the arc length formula,

  $\begin{array}{l}s=r\cdot \theta \\ s=4ft\cdot \frac{5\pi }{9}\\ s=\frac{20}{9}\pi ft\\ s=6.98feet\end{array}$

Conclusion:

The length of the arc is $6.98feet$ .