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’.
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 a1,
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)
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 –m1,
1 + m1 m2
By using this formula we find angles between two lines.
Example: - Find the angle between two lines m1 and m2, where the value of m1 = ½ and m2 = 2?
Solution: We know that the value of m2 is always equal to the value of m1.
Given, m1 = ½ and m2 = 3.
The formula for finding the angle between two lines:
tan∅ = m2 –m1,
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
tan∅ = 1.