Measure Arc Length

Arc length is defined as the distance along the curved line making up the arc. It is longer than the straight line distance between the end points along the curved line. The arc length is the length of this "portion" of the circumference of the circle. But the circumference itself can be considered as arc length. Various methods are available for the calculation of the measure of arc length. The two arcs can be adjacent arcs when

1. Do not overlap, and

2. Share a common end point.

 My forthcoming post is on Arc Length Equation, Points Lines and Planes will give you more understanding about Geometry.

measure of arc length

Where,

L is the measure of  arc length.

r is the radius of arc.

Theta is the central angle
Formula to Find the Measure of Arc Length:

Central angle in degrees

The formula for arc measure is:

Measure of arc length = (`(2 * Pi * R * c)/(360)` )

Where,

C is the central angle of the arc in degrees

R is the measure of radius of the arc.

We know that 2pR is the circumference of the full circle, so in the simpler form the formula reduces this as the ratio of the arc angle to the full angle of circle angle (360). By knowin any of the above things we can be able to calculate the arc length.

Central angle in radians

If the central angle is is expressed in radian, then the formula is :

Arc Length = RC

Where:

C is the central angle of the arc in radians.

R is measure of radius of arc

This is the same as the formula expressed in degrees, but in the degrees formula, the 2p/360 converts the degrees to radians.

Minor and Major arcs:

Given that two points on a circle, the minor arc is the shortest arc linking these two points. The majorarc is the longest. If we know any one of them we can find the rest one by using the formula,

Circumference of circle = Major arc length + Minor arc length.

Since these two arcs lie on the circumference of the circle the sum of these two arc.
Example Problems on Measure Arc Length:

1. Given that radius =5cm and central angle = 30 degrees. calculate arc length.

Arc length= (`(2 *5 *30)/(360)` )= 0.83cm

2. Given radius of arc =10cm and central Angle=120 degree. calculate arc length

Arc length= (`(2 * 10*120)/(360)` )= 6.66 cm.

3. Given Angle of arc = 3 radians and radius of arc = 10cm. calculate arc length

Arc length= 10x3= 30cm.
Practice problems:

Having problem with help factoring polynomials keep reading my upcoming posts, i will try to help you.

Calculate The Arc length of the following,

1. Given Central Angle= 20 degree and radius of arc = 10cm (Arc length=1.11cm)

2. Given Central Angle= 1.5 radians and radius of arc = 4cm (Arc length=6cm)

3. Given Central Angle= 1 radians and radius of arc = 2.5cm (Arc length=2.5cm)