A part of a curve or a part of a one of a one is referred to as Arc.All of lock havea curvein their shape. The curved section of this objects is mathematically called an arc. Arclength is better defined as the distance follow me the part of the one of any circle or any curve (arc). Any kind of distance along the bent line that provides up the arc is well-known as the arc length. The length of one arc is longer than any kind of straight heat distance in between its endpoints (a chord).

You are watching: Length of a curve between two points

1. | What is Arc Length? |

2. | Arc size Formula |

3. | How to uncover Arc length of a Curve? |

4. | FAQs top top Arc Length |

## What isArc Length?

Thearc length is defined as the interspace in between thetwo points along a section of a curve. Anarcof acircleis any part of the circumference. Theangle subtended by an arcat any allude is the edge formed between the two line segments joining that allude to the end-points the the arc. For example, in the circle shown below, OP is the arc that the one with facility Q. The arc length of this arc OP is provided as L.

## Arc size Formula

The length of an arc can be calculate using various formulas, based on the unit that the centralangle of the arc. The measurements of the main angle deserve to be provided in degrees or radians, and accordingly, we calculate the arc length of a circle.For acircle, the arc length formula isθ time theradius that a circle.

The arc length formula in radians have the right to be express as, arc size = θ × r, whenθis in radian. ArcLength = θ × (π/180) × r, whereθis in degree, where,

L = length of anArcr = Radius the the circle### Arc length Formula in Radians

The arc length of a circle have the right to be calculate using different formulas, based upon the unit of the center angle of the arc. The arc length formula in radians can be express as,

ArcLength = θ × r

where,

L = Arc Lengthθ = center angle of the arc in radiansr = Radius of the circle## How to find Arc length of a Curve?

The arc size of an arc the a circle have the right to be calculation using different methods and formulas based on the offered data. Some important instances are provided below,

find arc length with the radius and main anglefind arc size without the radiusfind arc size without the central angle

### How to discover Arc size With the Radius and central Angle?

The arc size of a circle can be calculated through the radius and central angle using the arc length formula,

Length of one Arc = θ × r, whereθis in radian.Length of an Arc= θ × (π/180) × r, whereθis in degree.### How to find Arc size Without the Radius?

The arc length of a circle have the right to be calculated there is no the radius using:

**Central angle and the sector area:**

Example: calculation the arc length of a curve with sector area 25square units and the central angle as 2 radians.

We have,

Sector area = 25 units

Central edge =2 radians

**Step 1:**Sector area × 2 = 25× 2 = 50

**Step 2:**50/central edge = 50/2= 25

**Step 3:**√25 = 5

**Step 4:**5× central angle =5× 2

**= 10 units**

Thus, arc size = 10 units

**Central angle and the chord length:**

**Example**: calculate the arc length of a curve, whose endpoints touch a chord the the one measuring 5 units. The central angle subtended by the arc is2 radians.

We have,

Chord length = 5 units

Central angle =2 radians

**Step 1:**Central angle/2 = 2/2 = 1

**Step 2:**Sin(1) =0.841

**Step 3:**Chord length/ (2× 0.841) = 5/ 1.682 = 2.973 systems = radius

**Step 4:**Arc length = radius × central angle = 2.973× 2 = 5.946 units

Thus, arc length = 5.946 units

### How to discover Arc size Without the central Angle?

The arc size of a circle can be calculated there is no the angleusing:

**Radius and the ar area**:

Example: calculate the arc size of a curve v sector area 25square units and also radius together 2 units.

We have,

Sector area = 25 units

Central angle =2 units

**Step 1:**Sector area × 2 = 25× 2 = 50

**Step 2:**50/radius2 = 50/4= 12.5 = main angle(rad)

**Step 3:**Arc length = radius× central angle = 2× 12.5

**= 25units**

Thus, arc size = 25units

**Radius and also chord length:**

**Example**: calculation the arc size of a curve, whose endpoints touch a chord the the circle measuring 5 units. The radius the the circleis2 units.

We have,

Chord length = 5 units

Central angle =2 units

**Step 1:**Chord length/(2× radius) = 5/(2× 2) = 1.25

**Step 2:**Sin-1(1.25) =0.949

**Step 3:**Central edge = 2× 0.949= 1.898radians

**Step 4:**Arc length = radius× central angle = 2× 1.898

**= 3.796units**

Thus, arc length = 3.796units

### Important Notes

Given listed below are key highlights top top the ide of arc length.

Arc size = θ × r, whereθis in radian.Arc length = θ × (π/180) × r, whereθis in degree.**Related subject on Arc Length:**

**Example 1: find the size of an arc cut off by a main angle the 4 radians in a circle v a radius that 6 inches.See more: What Term Best Represents The Resiliency Of A Cryptographic Key To Attacks?**

**Solution:**

Center angle, θ = 4radians, radius, r = 6 inch . Use the arc lengthformula,L = θ × r= 4 × 6= 24 inches. ∴ Arc length(PQ) = 24inches

**Example 2:Find the length of one arc cut off by a main angle,θ = 40º in a circle v a radius the 4inches.**

**Solution:**

Radius, r = 4inches , θ = 40º. Usage the arc lengthformula,L = π× (r) × (θ/180º)= π × (4) × (40º/180º)= 2.79inches. ∴ Arc length(P0) = 2.79inches