Simulation · Maths · Class 11
The angle between two lines
From the lesson Angle between two lines in Straight Lines. Change the values and watch what happens.
The angle between two linesMaths · Class 11
The idea behind it
NCERT §9.2.3
- Two intersecting lines make two pairs of vertically opposite angles, and adjacent angles add to 180°. If the lines have slopes m₁ and m₂, the angle θ = α₂ − α₁ between them has tan θ = (m₂ − m₁)/(1 + m₁m₂).
- Taking the modulus gives the acute angle: tan θ = |(m₂ − m₁)/(1 + m₁m₂)|, provided 1 + m₁m₂ ≠ 0. The obtuse angle is 180° − θ.
- If 1 + m₁m₂ = 0, the lines are perpendicular and θ = 90°.
- Example: lines of slopes 1 and 0 make tan θ = 1, an angle of 45°. Lines of slopes 2 and 3 make tan θ = 1/7.
- If the angle between two lines is π/4 and one slope is 1/2, then |(m − 1/2)/(1 + m/2)| = 1, which gives m = 3 or m = −1/3. There are two answers because the second line can be turned either way from the first.