Arc Length and Radian Measure Worksheets
This section helps us learn to further explore geometric circles. We learn how to measure specific portions of circles. Most of this is based on the concept of circumference which is the full length of the circle curvature. We measure this curvature in units of degrees, but we also explore the use of radian measures that are rooted on this topic. We also show you how transition between these two forms of measure. These worksheets and lessons teach students how to determine the length of the arc of a circle and the measure in radians.
Aligned Standard: HSG-C.B.5
- 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.
- Answer Keys - These are for all the unlocked materials above.
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.
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.
Math Skill Quizzes
How would you go about using these as a daily warm up. It's a good idea!
- Quiz 1 - What a huge advantage to look at it from that stance?
- Quiz 2 - Don't just warm up take it all the way!
- Quiz 3 - I never knew how important the circle was until now.
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 length of a curvature. An arc measure provides a value for how much of the arc is around the center of a circle. Angles can be measured in radians or degrees. Degree measures are the most popular to use. This is commonly based on the concept of a complete circle encompassing 360 degrees. You can convert degrees to radians by multiplying the measure is degrees by Π / 180.
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.
What is the Radian Measure of an Angle?
Angles, in general, are measures of the amount of rotation that is required to reach one of the sides to the other. Radian measures take into account the concept of looking at this angle encompassed within a circle. It positions the angle as a central angle of the circle, where the vertex of the angle is positioned in the center of it. One radian is the measure of the arc that is formed by extending the lines of the angle to the edge of the circle. The circumference of a circle can be calculated using the formula 2Πr. We can relate that to measuring in degrees because 360° = 2Πr.