Answer:
The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.
Step-by-step explanation:
Geometrically speaking, we determine the arc length ([tex]s[/tex]), in inches, and the area ([tex]A[/tex]), in square inches, of a circle sector by means of these formulas:
[tex]s = 2\pi\cdot \left(\frac{\theta}{360}\right)\cdot r[/tex] (1)
[tex]A = \pi \cdot \left(\frac{\theta}{360} \right)\cdot r^{2}[/tex] (2)
Where:
[tex]r[/tex] - Radius, in inches.
[tex]\theta[/tex] - Central angle, in sexagesimal degrees.
If we know that [tex]\theta = 40^{\circ}[/tex] and [tex]r = 13\,in[/tex], then the arc length and the area of the circle sector are, respectively:
[tex]s = 2\pi\cdot \left(\frac{40}{360} \right)\cdot (13\,in)[/tex]
[tex]s \approx 9.076\,in[/tex]
[tex]A = \pi \cdot \left(\frac{40}{360} \right)\cdot (13\,in)^{2}[/tex]
[tex]A = 58.992\,in^{2}[/tex]
The arc length and the area of the circle sector are approximately 9.076 inches and 58.992 square inches.
