A circle has a central angle measuring StartFraction 3 pi Over 4 EndFraction radians that intersects an arc of length 45 in. What is the length of the radius of the circle? Round your answer to the nearest tenth. Use 3.14 for Pi.

r = 19.1 in

Step-by-step explanation:

Given:-

- The central angle of a circle, θ = 3π / 4

- The arc length, s = 45 in

Find:-

What is the length of the radius (r) of the circle?

Solution:-

- The arc length (s) of a sector of circle with a radius (r) subtended by a central angle (θ) is expressed by the given relation:

s = r * θ

- Plug in the values and solve for radius (r)

r = s / θ

r = 45 / (3π / 4) = (45*4) / (3*3.14)

r = 19.1 in

Answer: The radius measures 19.1 inches (approximately)

Step-by-step explanation: The central angle in the sector has been given as 3Pi/4 radians. We start by converting the radians to degrees.

1 radian = 180/Pi (or 57.296 degrees)

Hence 3Pi/4 converted to degrees becomes,

= 3Pi/4 x 180/Pi

= (3 x 180) / 4

= 135

Having determined the central angle to be 135 degrees, and the length of the arc is 45 inches, the radius can be calculated by substituting for the values into the formula for length of an arc.

Length of an arc = (X/360) x 2Pi x r

45 = (135/360) x 2 (3.14) x r

45 = (3/4) x 3.14 x r

By cross multiplication we now have

(45 x 4) / 3 x 3.14 = r

180/9.42 = r

19.1083 = r

Therefore, the radius rounded to the nearest tenth equals 19.1 inches.