units

60/360 * diameter * π

radius * 2 = 9* 2 =18

60/360 =1/6 * 18π

360x= 3391.2

360x= 4710

Find the arc length of a circle with a central angle of 75 degrees and a radius of 10 units.

The **arc length formula** can be used to calculate the **radius** of a circle. Basically you plug in the given information into the arc length formula, and solve for the radius. If the central angle is given in radians use: s = θ*radius

θ = measure of the central angle

If the central measure is in degrees use:

Measure central angle/360 =arc length/circumference (dπ)

0:53 Problem 1. Finding the radius of a circle in radians.

If an arc length measures 4π inches long, with a central angle of π/3, find the length of the radius.

2:00 Solution problem 1

2:16 Find the radius of a circle in degrees.

Given the arc length of 8π and a central angle of 120◦, find the radius.

4:29 Solution problem 2

Point of Reference

What is the length of an arc subtended by an angle of 7π/4 radians on a circle with a radius 10 units?

θ

20

Minor Arc

Major Arc

Θ = measure of the central angle

Arc Length and Radian Measure/Regents Prep Short lesson covering arc length of a circle along with an explanation of degrees and radians, and several sample problems calculating arc measure.

Circles and Arcs/Khan Academy A video,interactive sketchpad, and sample questions covering arcs of circles.

Arc Length Calculator Check your homework with this calculator

θ

What is the **length of the arc** from A to B of a circle that has a central angle measure of 60 degrees and a radius of 9 units ?

In a circle congruent **central angles** will have **congruent arcs** and **congruent arcs** will have **congruent central angles**

The measure of an **arc** is equal to the **measure of the central angle** that intercepts the arc.

θ

Finding the arc length explained

- Distance from
**A**to**B**= the arc length.

- Any two points on a circle except two points exactly opposite each other create a minor and major arc.

- The
**minor arc**has a smaller angle measure and length than the**major arc.**

The arc length of a circle is distance along the curved portion of a circle or any other curve. The arc length is longer than a chord which is a straight line distance between the endpoints. The circumference of a circle is considered an arc length with a measure of 360 degrees.
A chord is defined as a straight line that intersects a circle at two points. The diameter of a circle is a chord that cuts a circle in half.
The letter s is traditionally used to represent arc length. The s stands for subtends which means “opposite of.” A subtended angle is an angle created by an arc or any other object from a given point of view.