Question

A circle has a central angle measuring 90° that intersects an arc of length 117.75 inches.Using 3.14 for pi, what is the length of the radius of the circle?

Answer 1

I hope this helps you




Arc Length=Center Angle/360.2.pi.r



117,75=90/360.2.3,14.r



r=117,75/1,57


r=75

Answer 2

The formula for arc length of a circle is given by:

Arc length = $\frac{x}{360}*2\pi r$

Where,

• x is the intercepted central angle
• r is the radius

Putting x=90° into this formula and 117.75 into arc length, and solving for r, gives us:

$\frac{90}{360}*2 \pi r=117.75\\(0.25)*2(3.14)r=117.75\\1.57r=117.75\\r=\frac{117.75}{1.57}=75$

Hence, the radius is 75 inches.

ANSWER: 75 in