Question

A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches.

Answer 1

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 .

Answer 2

90 degrees is one quarter of a circle so,
circumference = 4 * 117.75 = 471
circumference = 2 * PI * radius
radius = 471 / (2*PI)
radius = 74.9619781963