## Arc Length and Radian Measure

#### Aligned To Common Core Standard:

**High School Geometry** - HSG-C.B.5

How to Calculate the Length of an Arc - An arc is typically defined as the small segment present at the circumference of a circle. Or any fraction of circle's circumference lying between two points. Arc span is defined as the span along the arc. An arc measure is the angle made arc at the center of a circle. The angle is measured in radians or degrees. You can easily figure out the arc of the circle by taking less than full length around the circle within two radii. We use the following formula for calculating the length of an arc: arc measure= (arc length)/radius = s/r Let's understand it better with an example. If our arc length is 3cm and our radius is 4 cm. Write down the formula first: arc measure =s/r | arc measure = 3/4| This is written in radians; we can have it degrees by multiplying it with 180/ π = (3/4) (180/π) = 42.971 = 43 degrees. These worksheets and lessons teach students how to determine the length of the arc of a circle and the measure in radians.

### Printable Worksheets And Lessons

- Angles to Radians Step-by-Step Lesson- A simple conversion and I provide all the background that you need.
- Guided Lesson - Time for Pi! Not the tasty dessert .
- Guided Lesson Explanation - These were actually very fun to work through. I missed Trig, if that doesn't sound weird.
- Practice Worksheet - Straight working with conversion between systems.
- Matching Worksheet - Match the conversion between radians and degrees.

#### Homework Sheets

A number of different conversion strategies are set for you over the course of this series.

- Homework 1 - The length of an arc is simply the length of its "portion" of the circumference.
- Homework 2 - A radian is the measure of an angle ø that, when drawn as a central angle, subtends an arc whose length equals the length of the radius of the circle.
- Homework 3 - Convert 20° to radians.

#### Practice Worksheets

Many teachers write in and let us know that these were very helpful for them.

- Practice 1 - Pi radians to degrees, what is that all about?
- Practice 2 - Actually, the circumference itself can be considered an arc length.
- Practice 3 - Arc lengths take a bit of time to comprehend.