The question is...find the radian measure of the central angle of a circle of radius r that intercepts an arc of length s. Then it gives the radius r of 27 inches and an arc length s of 6 inches. How do I do that?
you should have come across the formula
arc length = r(theta), where theta is the central angle
6 = 27theta
theta = 6/27 radians
= 2/9 rad
To find the radian measure of the central angle, you need to use the formula:
θ = s / r
where θ represents the central angle in radians, s represents the length of the intercepted arc, and r represents the radius of the circle.
In your case, the radius (r) is given as 27 inches, and the arc length (s) is given as 6 inches. Plugging these values into the formula:
θ = 6 / 27
Now, divide 6 by 27:
θ ≈ 0.222 radians
Therefore, the radian measure of the central angle that intercepts an arc of length 6 inches on a circle with a radius of 27 inches is approximately 0.222 radians.
To find the radian measure of the central angle of a circle, you can use the following formula:
θ = s / r
where
θ is the radian measure of the central angle,
s is the length of the intercepted arc, and
r is the radius of the circle.
In your case, the radius is given as 27 inches and the arc length is given as 6 inches. Plugging these values into the formula, we have:
θ = 6 / 27
Simplifying this expression, the radian measure of the central angle is:
θ ≈ 0.222 radians