Answer:
Radius = 75 inches .
Step-by-step explanation:
Given : A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches.
To find : what is the length of the radius of the circle.
Solution : We have given
Central angle = 90°
Arc of length = 117.75 inches.
Arc length = \(\frac{theta}{360}* 2 \pi * radius\).
Plug the values
Theta = 90 , pi = 3.14 , arc length = 117.75 .
117 .75 = \(\frac{90}{360}* 2(3.14 ) * radius\).
117 .75 = \(\frac{1}{4}* 2(3.14 ) * radius\)
On multiplying both sides 4
117.75 4 = 2 3.14 radius .
471 = 6 .28 radius .
On dividing both sides by 6.28
radius = \(\frac{471}{6.28}\).
Radius = 75 inches .
Therefore, Radius = 75 inches .
