# Angle between two lines Calculator

# Angle between two lines Calculator

The calculator for finding the angle between two lines requires the input of the slope of the two lines. The formula for finding the angle between two lines is given by:

$ \theta = \tan^{-1} \left( \left| \frac{m_2-m_1}{1+m_1m_2} \right| \right) $

where $m_1$ and $m_2$ are the slopes of the two lines.

In order to use this formula, you first need to find the slopes of the two lines, which can be done using the formula:

$m = \frac{y_2 – y_1}{x_2 – x_1}$

where $(x_1,y_1)$ and $(x_2,y_2)$ are two points on the line. Once you have found the slopes, you can input them into the angle between two lines formula to get the result.

## The angle between two lines with example

The angle between two lines can be calculated using the formula:

**θ = tan⁻¹(m₂ – m₁ / 1 + m₁m₂)**

Where m₁ and m₂ are the slopes of the two lines.

Let’s take an example to understand this better:

**Find the angle between the lines y = 3x – 4 and y = 2x + 1.**

**Solution:**

To find the angle between the lines, we need to calculate the slopes of both lines.

Slope of the first line (m₁) = 3 Slope of the second line (m₂) = 2

Now, we can substitute these values in the formula:

**θ = tan⁻¹(2 – 3 / 1 + (3 x 2)) = tan⁻¹(-1 / 7) ≈ -8.13°**

Therefore, the angle between the lines y = 3x – 4 and y = 2x + 1 is approximately -8.13 degrees. Note that the angle is negative because the lines are moving in opposite directions.