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2 years ago

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

Mathematics

2 answers:

olga_2 [115]2 years ago

7 0

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 .

pychu [463]2 years ago

5 0

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

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