What measure is obtained by dividing the length of the arc by the radius?

The measure obtained by dividing the length of an arc by the radius of the circle is radians. In geometry, a radian is defined as the angle formed when the length of the arc is equal to the radius of the circle. Therefore, if you take the length of the arc and divide it by the radius, you get the angle in radians, which is a fundamental unit of angular measurement.

For instance, if the length of the arc is equal to the radius, the angle is one radian. This relationship is essential in trigonometry and helps with conversions between different angle measurements. Understanding this concept is crucial for various applications in surveying and applied mathematics, as it allows for more seamless calculations when working with angles and circular measurements.