Find the radius if the length of an arc is 23.56 and the angle is 135 degrees.
C = r*theta
23.56 = r * 3pi/4
r = 23.56 * 4/3pi
To find the radius of a circle given the arc length and angle, you can use the following formula:
radius (r) = (arc length (s) * 180) / (angle (theta) * π)
Given:
Arc length (s) = 23.56
Angle (theta) = 135 degrees
First, convert the angle from degrees to radians by multiplying it by π/180:
theta (in radians) = 135 * π/180 = 2.356 radians
Now, substitute the given values into the formula:
radius (r) = (23.56 * 180) / (2.356 * π)
To find the value of π, you can either use the approximation 3.14 or a more accurate value like 3.14159.
Using 3.14:
radius (r) = (23.56 * 180) / (2.356 * 3.14) ≈ 476.62 / 7.39864 ≈ 64.43
Using more digits of π:
radius (r) = (23.56 * 180) / (2.356 * 3.14159) ≈ 476.62 / 7.38871 ≈ 64.50
Therefore, the radius of the circle is approximately 64.43 (or 64.50) units.