Circles and arcs

The  exercise appears under the Geometry Math Mission. This exercise introduces the arc length formula in radians and degrees.

Types of Problems
There are two types of problems in this exercise:


 * 1) Find the length of the arc: This problem provides a diagram with a circle and the measure of a central angle. The student is expected to find the length of the arc and write it in the space provided.Caa1.png
 * 2) Find the length of the arc: This problem provides a diagram with a circle and the measure of an arc. The student is expected to find the angle measure and write it in the space provided.Caa2.png

Strategies
Knowledge of the arc length formula, in both radians and degrees, is encouraged to ensure success on this exercise.
 * 1) The arc length formula in radians is $$s=r\theta$$. In degrees it is $$s=\frac{\theta}{360}2\pi r$$.
 * 2) The formula for arc length is not vital to know. These problems can also be set of with knowledge of circumference ($$C=2\pi r$$), and the ratio mnemonic "part to whole."

Real-life Applications

 * 1) Arc length is important for finding lengths along circular objects, such as the path of a pendulum.
 * 2) Arc length is connected with the differences between angular and linear velocity which leads into certain physics accelerations on circles.
 * 3) Problems involving arc length and sector area are common on standardized tests, such as the ACT and SAT.