The sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
For a sector that has a central angle of θ, and a radius of r;
The sector area, and the arc length are:
[tex]A = \frac{\theta}{360} * \pi r^2[/tex] --- sector area
[tex]L = \frac{\theta}{360} * 2\pi r[/tex] ---- arc length
Here, the given parameters are:
Central angle, θ = 160
Radius, r = 5 inches
The sector area is
[tex]A = \frac{\theta}{360} * \pi r^2[/tex]
So, we have:
[tex]A = \frac{160}{360} * \frac{22}{7} * 5^2[/tex]
Evaluate
A = 34.92
The arc length is:
[tex]L = \frac{\theta}{360} * 2\pi r[/tex]
So, we have:
[tex]L = \frac{160}{360} * 2 * \frac{22}{7} * 5[/tex]
L = 13.97
Hence, the sector area and the arc length are 34.92 square inches and 13.97 inches, respectively
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