 # Radian, Arc Length and Sector Area

Videos and lessons to help High School students learn how to derive using similarity the fact that the length of the arc intercepted by an angle is proportional to the radius, and define the radian measure of the angle as the constant of proportionality; derive the formula for the area of a sector.

Common Core: HSG-C.B.5

Arc Length of a Sector of a Circle using Radian Measurement
This video uses the definition of Radian measurement of angles in order to calculate the arc length of a sector of a circle.
Radians as Proportionality Constants
An angle measure in radians can be defined as the constant of proportionality in the relationship between the radius and the intercepted arc.
? = s/r
s = r ?

Arc Length and Area of a Sector
How to determine arc length and how to find the area of a sector.
A = 1/2 r2 ?

Radians, Arc Length & Sector Area
An introduction to the measure of radians and two commonly used radian formulas for the arc length and the sector area of a circle.

Investigate Area of a Sector and Arc Length
Rotate point C counterclockwise to change angle A, and move point B to change the radius.
1) What is the relationship between the circumference of the circle and 1 revolution? What is the relationship between the arc length s and the angle theta? Derive the equation.
2) What is the relationship between the area of the circle and 1 revolution? What is the relationship between the area of the sector and the angle theta? Derive the equation.

Try the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.  We welcome your feedback, comments and questions about this site or page. Please submit your feedback or enquiries via our Feedback page.