How to Find the Angle between two Lines?

  The Intersection between two lines defines an Angle between two lines. Here we will see how to find the angle between two lines.

For finding the angle between two lines we have to follow some of the steps:

Step1: First assume the angle between two lines.

Step2: Then we have to find the value of slopes of the given lines. Let the line be ‘L₁’ and ‘L₂’.

Step3: Now we have to find the Tangent difference between the two angles by using trigonometric Functions.

Step4: Using these steps we get the angle between two lines.

We know that,

  a₂ = a₁ + ∅,

    ∅ = a₂ – a₁,

Now we determine the value of slopes of line ‘L₁’ and ‘L₂’.

By using trigonometric Functions:

 tan∅ = tan (a₂ – a₁),

             = tan a₂ - tan a_1,

                1 + tan a₁ tan a₂

If tan a₁ = m₁ (m₁ is the Slope of the line l₁)

   tan a₂ = m₂ (m₂is the Slope of the line l₂)

So that,

           The value of ‘m₂’ is greater than ‘m₁’, (m₂ > m₁).

Substitute these values in the given equation.

On putting these values we get:

 Tan ∅ = m₂ –m_1,

              1 + m₁ m₂

By using this formula we find angles between two lines.

Example: - Find the angle between two lines m₁ and m_2, where the value of m₁ = ½ and m₂ = 2?

Solution: We know that the value of m₂ is always equal to the value of m_1.

              Given, m₁ = ½ and m₂ = 3.

The formula for finding the angle between two lines:

 tan∅ = m₂ –m_1,

            1 + m₁ m₂

Putting the value of m₁ and m₂ in the given formula:

 Tan ∅ = 3–½,

              1 + ½ * 3

          = (6 - 1)/2,

            (2 + 3)/2

         = 5/2,

            5/2

     tan∅ = 1.