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A circle has a radius of 48 millimeters. What is the central angle in radians, that intercepts an arc of length 36π millimeters?

2 Answers

7 votes
arc length= radius x angle
36pie=48 x angle
divide both side by 48
you get 3/4pie
User Steve Moser
by
5.7k points
3 votes

Answer:


\theta=(3\pi)/(4)

Explanation:

The formula for length of intercepted arc is


s=r\theta

where, r is the radius of the circle and θ in the central angle in radian.

Radius of the circle = 48 millimeters

Length of intercepted arc = 36π millimeters

Substitute the given values in the above formula.


36\pi=48\theta

Divide both sides by 48.


(36\pi)/(48)=(48\theta)/(48)


(3\pi)/(4)=\theta

Therefore, the measure of central angle is
\theta=(3\pi)/(4).

User Alextunyk
by
5.6k points