Problem 109 - Algebra and Trigonometry

Question

Explain how to find the length of a circular arc.

Step-by-Step Solution

Answer

To find the length of a circular arc, divide the angle in degrees that the arc makes up by 360, then multiply the result by the circumference of the circle (which can be found using the formula \(2\pi r\)).

Step 1: Understand the Problem

Realize that the problem is asking for the length of an arc of a circle, which can be found using the formula for the circumference of a circle and some knowledge about angles.

Step 2: Calculate the Ratio of the Angles

First calculate the ratio of the angle \(\theta\) in degrees of the arc to the total angle in a circle which is 360 degrees. This is done by simply dividing \(\theta\) by 360.

Step 3: Find the Circumference of the Circle

The next step is to find the circumference of the circle, the formula for which is \(2\pi r\), where \(r\) is the radius of the circle.

Step 4: Calculate the Arc Length

Finally, multiply the result of the angle ratio by the circumference of the circle to find the length of the arc.