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## Measures of Arc Length

#### Circles - HSG-C.B.5

How to find the Measurements of Arcs? We know what a circle is. It is a round figure that goes 360 degrees all the way around. There are lots of terms related to the circle and one such term is called an arc. A segment of the circle around its circumference is known as the arc and its span along the arc is known as arc length. An angle formed in the middle of the circle by the arc is known as the arc measure. Angles have two units of measures. The first unit is degrees, and degrees of angles represent the same fraction of the circle as its corresponding arc. For example, if you say 1/4th of the circle, the angle will be 90 degrees. So the arc of a 90-degree circle will represent 14th of the circle. The second unit is known as radian. By following two rules, we can convert radians into degrees. Remember that a full circle is 360 degrees or 2π radians. A single radian is equal to 180 degrees. For conversion of radian into degrees, we multiply the radian measure by 180/π. For the conversion of degrees into radians, we multiply the degree measure by π/180. Let's say we need to find the radian measure of 70 degrees. So, 70 multiplied by π/180 = 1.22 radian. These worksheets and lessons help students learn how to determine and predict the measure of arcs.

### Printable Worksheets And Lessons  #### Homework Sheets

Find the length of various arcs in many different exercises.

• Homework 1 - Where l is the arc length, C is the circumference, and m is the measure of the arc in degrees.
• Homework 2 - This one is pitched at a 30 degee angle. We give you a completed problem to work with, in case you fogot the basic procedure.
• Homework 3 - Once you have the circumference just pop it into the equation.

#### Practice Worksheets

Knowing how to properly apply the arc formula is easier said than done for most students.

• Practice 1 - The radius of a circle is 10 inches. What is the length of a 180 degrees arc?
• Practice 2 - Start with finding the circumference. We are looking to find the measures of blue sections.
• Practice 3 - The formula for the length of an arc is l = m/360 degrees x c.

#### Math Skill Quizzes

We master moving between radians and degrees. As you practice this skill, it gets easier.

• Quiz 1 - Convert π /8 radians to degrees. Then convert it back again.
• Quiz 2 - Convert 220° to radian measure. We also go back and look at the other skill as well.
• Quiz 3 - This is all in one. A nice big quiz. Six questions will keep you busy for a while.

### How Does This Measure Apply to Real Life?

When we start working with circles it is difficult to see how this applies to your everyday life. You would be surprised by the sheer volume of application that this skill actual has. Just about any situation where you have a fixed object that travels in a circular pattern around where it is attached can be modelled in this manner. Think about a swing set. We all love to swing! Have you ever wanted to figure out how far you are actually travelling on that swing? Guess what formula can help you figure that out? What about situations where you are hurling an object? If you were to hurl a shot put as far as you possibly can, wouldn’t it a great idea to know where you should release that object to maximize the distance that it travels? Photographers are experts on circle geometry since their lens are entirely based on this principal. They quickly learn that the quality of their images relates to the diameter of their lens and the focal length. Ship navigation is entirely dependent on this type of math as well. Have you ever seen a sonar output? Give it a quick Internet search. You will see that they look just like the diagrams that you see on the worksheets above.