To determine the length of an arc given a radius and a central angle, the formula is:
[tex]ArcLength=\frac{\theta}{180}\times\pi r[/tex]
The measure of the central angle for Arc RS is 150°. The radius of the circle is 6.48 inches.
Let's plug those values into the formula above.
[tex]ArcLength=\frac{150}{180}\times3.14\times6.48in\text{ }[/tex]
Then, solve.
1. Divide 150 by 180 first.
[tex]ArcLength=0.8333333\times3.14\times6.48in[/tex]
2. Multiply all three terms.
[tex]ArcLength=16.956in\approx17.0in[/tex]
Hence, the length of Arc RS is 17.0 inches.
