User:Asillacad

Arc Length of a Circle
An arc length is simply the measurement of a section of the circumference of a circle if it were to be stretched out into a straight line. An arc length could even be the circumference of a circle. Arc length is represented by the letter s. It is important to acknowledge that arc length is usually answered with radians and not degrees.

Dumb it down Imagine a pumpkin pie. Now cut that pie into 5 pieces. Focus on one slice of that pie and look at the crust. How would you measure the length of the crust? Well, the crust of that pie slice is a section of the circumference so it should also be known as an arc length.

The equation to find arc length, S, is

S= rθ

The letter r stands for the radius of the circle, and θ stands for the measure of the angle in radians. The measure of the angle in radians can be found using

D/R=180°/π

How to apply it

Find the arc length of a circle with a radius of 3, and an angle measure of 60°.

First, list the information you have

s=?

r=3

angle measure= 60°

Secondly, change the angle measure into radians

1) 60°/R=180°/π

2) cross multiply,    60°·π = 188.4955592

3)Divide the answer by 180°

188.4955592/ 180° = 1.0471

Thirdly, substitute the information you have into the arc length formula

s=?

r=3

θ=1.0471

So,

s = 3·1.0471

Fourth

Real World

Autumn is bored in class and is staring at the clock. She wonders what the distance is from the hand on the 2 to the hand on the 3. She assumes that the angle created by the hands is 30°. She wonders, though, what the distance between the 2 and the 3 is. Figure it out for her while she waits for the class to end.

1) S=3θ

2) 30°/R = 180°/π

3) 30·π = 94.24777961

4) 94.24777961/180° = 0.5235987756

So the arc length, or the distance between 2 and 3, is 0.5235987756 units.