In a circle with radius of 7 cm, an arc of the circle has length 22 cm.
The central angle theta is ??
Angle θ = arc length / radius,
=22/7
= π approx. (in radians).
To find the central angle theta, we can use the formula:
Arc length = (Central angle / 360) * (2 * pi * Radius)
Given:
Arc length = 22 cm
Radius = 7 cm
Let's plug in the values and solve for theta:
22 cm = (Central angle / 360) * (2 * pi * 7 cm)
First, simplify the equation:
22 cm = (Central angle / 360) * (14 * pi cm)
Next, let's get rid of the fraction by multiplying both sides of the equation by 360:
22 cm * 360 = Central angle * (14 * pi cm)
7920 cm = Central angle * 14 * pi cm
Divide both sides of the equation by (14 * pi) to solve for the central angle:
Central angle = (7920 cm) / (14 * pi cm)
Finally, simplify the expression:
Central angle = 180 cm / pi
Therefore, the central angle theta is approximately equal to 57.3 degrees.