What is the formula for finding the central angle of a sector when given the radius and arc length?
s = rθ, so θ = s/r
The formula for finding the central angle of a sector when given the radius and arc length is:
Central Angle (in radians) = Arc Length / Radius
You can convert the value from radians to degrees by using the formula:
Central Angle (in degrees) = Central Angle (in radians) * (180 / π)
So, the step-by-step process is:
1. Divide the arc length by the radius to find the central angle in radians.
2. If you want the answer in degrees, multiply the central angle in radians by (180 / π) to convert it to degrees.
To find the central angle of a sector when given the radius and arc length, you can use the following formula:
Central Angle = (Arc Length / Radius) * (180° / π)
Here's an explanation of how to use this formula:
1. Determine the unit of measurement used for the arc length and radius. Make sure both measurements are in the same units (e.g., inches, meters, etc.).
2. Divide the arc length by the radius. This will give you the ratio between the length of the arc and the length of the radius.
For example, if the arc length is 10 units and the radius is 5 units, the ratio would be 10 / 5 = 2.
3. Multiply the ratio obtained in step 2 by the conversion factor (180° / π). This will convert the ratio from radians to degrees, and gives you the central angle in degrees.
The conversion factor, 180° / π, is used because there are 180 degrees in a π radians.
For example, if the ratio is 2, the central angle would be 2 * (180° / π) = (360° / π) radians.
Therefore, the formula for finding the central angle of a sector when given the radius and arc length is (Arc Length / Radius) * (180° / π).