Angle between a Pair of Lines

Last Updated : 07 May, 2021

Given two integers M1 and M2 representing the slope of two lines intersecting at a point, the task is to find the angle between these two lines.

Examples:

Input: M₁ = 1.75, M₂ = 0.27
Output: 45.1455 degrees

Input: M₁ = 0.5, M₂ = 1.75
Output: 33.6901 degrees

Approach: If ? is the angle between the two intersecting lines, then the angle ? can be calculated by:

tan? = |(M₂ - M₁) / (1 + M₁ * M₂)|
=> ? = tan^-1( |(M₂ - M₁) / (1 + M₁ * M₂)| )

Follow the steps below to solve the problem:

Initialize a variable, say A, to store the value of the angle between the two lines.
Using the above formula, find the value of tan(A) and update the value of angle A by taking the tan inverse of the angle.
Convert the angle from radian to degrees.
Print the value of A in degrees as the result.

Below is the implementation of the above approach:

C++

// C++ program for the above approach
#include <bits/stdc++.h>
using namespace std;

#define PI 3.14159265

// Function to find the
// angle between two lines
void findAngle(double M1, double M2)
{
    // Store the tan value  of the angle
    double angle = abs((M2 - M1)
                       / (1 + M1 * M2));

    // Calculate tan inverse of the angle
    double ret = atan(angle);

    // Convert the angle from
    // radian to degree
    double val = (ret * 180) / PI;

    // Print the result
    cout << val;
}

// Driver Code
int main()
{
    double M1 = 1.75, M2 = 0.27;

    findAngle(M1, M2);

    return 0;
}

Java

// Java program for the above approach
import java.util.*;
class GFG 
{
    static double PI = 3.14159265;

    // Function to find the
    // angle between two lines
    static void findAngle(double M1, double M2)
    {
      
        // Store the tan value  of the angle
        double angle = Math.abs((M2 - M1) / (1 + M1 * M2));

        // Calculate tan inverse of the angle
        double ret = Math.atan(angle);

        // Convert the angle from
        // radian to degree
        double val = (ret * 180) / PI;

        // Print the result
        System.out.println(val);
    }

    // Driver Code
    public static void main(String []args)
    {
        double M1 = 1.75, M2 = 0.27;

        findAngle(M1, M2);
    }
}

// This code is contributed by rrrtnx.

Python3

# Python3 program for the above approach
from math import atan

# Function to find the
# angle between two lines
def findAngle(M1, M2):
    PI = 3.14159265
    
    # Store the tan value  of the angle
    angle = abs((M2 - M1) / (1 + M1 * M2))

    # Calculate tan inverse of the angle
    ret = atan(angle)

    # Convert the angle from
    # radian to degree
    val = (ret * 180) / PI

    # Print the result
    print (round(val, 4))

# Driver Code
if __name__ == '__main__':
    M1 = 1.75
    M2 = 0.27

    findAngle(M1, M2)

    # This code is contributed by mohit kumar 29.

// C# program for the above approach
using System;
class GFG 
{
    static double PI = 3.14159265;

    // Function to find the
    // angle between two lines
    static void findAngle(double M1, double M2)
    {
      
        // Store the tan value  of the angle
        double angle = Math.Abs((M2 - M1) / (1 + M1 * M2));

        // Calculate tan inverse of the angle
        double ret = Math.Atan(angle);

        // Convert the angle from
        // radian to degree
        double val = (ret * 180) / PI;

        // Print the result
        Console.Write(val);
    }

    // Driver Code
    public static void Main()
    {
        double M1 = 1.75, M2 = 0.27;

        findAngle(M1, M2);
    }
}

// This code is contributed by ukasp.

JavaScript

<script>

      // JavaScript program 
      // for the above approach
      const PI = 3.14159265;

      // Function to find the
      // angle between two lines
      function findAngle(M1, M2) {
        // Store the tan value of the angle
        var angle = Math.abs((M2 - M1) / (1 + M1 * M2));

        // Calculate tan inverse of the angle
        var ret = Math.atan(angle);

        // Convert the angle from
        // radian to degree
        var val = (ret * 180) / PI;

        // Print the result
        document.write(val.toFixed(4));
      }

      // Driver Code
      var M1 = 1.75,
        M2 = 0.27;
      findAngle(M1, M2);
      
</script>

Output:

45.1455

Time Complexity: O(1)
Auxiliary Space: O(1)

Slope Intercept Form

portalpirate

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Angle between a Pair of Lines

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