Answer:
The length of the radius of the circle is 75 inches
Step-by-step explanation:
∵ A circle has a central angle measuring 90°
∵ The measure of the circle is 360°
- Divide the measure of the arc by the measure of the circle
to find that arc is represents what fraction of the circle
∵ 90 ÷ 360 = [tex]\frac{1}{4}[/tex]
∴ The arc represents [tex]\frac{1}{4}[/tex] of the circle
∵ The length of the circle = 2πr
∵ The arc represents [tex]\frac{1}{4}[/tex] of the circle
∴ The length of the arc = [tex]\frac{1}{4}[/tex] × 2πr
∴ The length of the arc = [tex]\frac{1}{2}[/tex] πr
∵ The length of the arc is 117.75 inches
- Equate the expression of the length of the arc by 117.75
∴ [tex]\frac{1}{2}[/tex] πr = 117.75
∵ π = 3.14
∴ [tex]\frac{1}{2}[/tex] (3.14) r = 117.75
∴ 1.57 r = 117.75
- Divide both sides by 1.57
∴ r = 75
∴ The length of the radius of the circle is 75 inches
