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 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.