Question

Find the measure of the central angle of an arc if its length is 7.1 and the diameter is 7.8. Round your answer to the nearest tenth.

Answer 1

The measure of the central angle is approximately 103.7 degrees.

Step-by-step explanation:

The measure of a central angle can be found using the formula:

θ = (s / r) * (180 / π)

Where θ is the measure of the central angle, s is the length of the arc, and r is the radius of the circle. In this case, the length of the arc is 7.1 and the diameter (which is equal to twice the radius) is 7.8. So the radius is 7.8 / 2 = 3.9. Plugging these values into the formula, we have:

θ = (7.1 / 3.9) * (180 / π)

Using a calculator, the value of θ is approximately 103.7 degrees. Rounded to the nearest tenth, the measure of the central angle is 103.7 degrees.