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Program to find third side of triangle using law of cosines

  • Difficulty Level : Medium
  • Last Updated : 25 Mar, 2021

Given two sides A, B and angle C. Find the third side of the triangle using law of cosines.
Examples: 
 

Input : a = 5, b = 8, c = 49 
Output : 6.04339 

 

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In particular, the Law of Cosines can be used to find the length of the third side of a triangle when you know the length of two sides and the angle in between. See here to learn to how to find the value of cos. 
Let us assume a, b, c are the sides of triangle where c is the side across from angle C. Then, 
 

c^2 = a^2 + b^2 - 2*a*b*cos(c) 
OR
c = sqrt(a^2 + b^2 - 2*a*b*cos(c))

 

 

C++




// CPP program to find third
// side of triangle using
// law of cosines
 
#include <bits/stdc++.h>
using namespace std;
 
// Function to calculate cos value of angle c
float cal_cos(float n)
{
    float accuracy = 0.0001, x1, denominator, cosx, cosval;
 
    // Converting degrees to radian
    n = n * (3.142 / 180.0);
 
    x1 = 1;
 
    // Maps the sum along the series
    cosx = x1;
 
    // Holds the actual value of sin(n)
    cosval = cos(n);
    int i = 1;
    do {
        denominator = 2 * i * (2 * i - 1);
        x1 = -x1 * n * n / denominator;
        cosx = cosx + x1;
        i = i + 1;
    } while (accuracy <= fabs(cosval - cosx));
 
    return cosx;
}
 
// Function to find third side
float third_side(int a, int b, float c)
{
    float angle = cal_cos(c);
    return sqrt((a * a) + (b * b) - 2 * a * b * angle);
}
// Driver program to check the above function
int main()
{
    float c = 49;
    int a = 5, b = 8;
    // function call
    cout << third_side(a, b, c);
 
    return 0;
}

Java




// Java program to find third
// side of triangle using
// law of cosines
class GFG
{
    // Function to calculate
    // cos value of angle c
    static float cal_cos(float n)
    {
        float accuracy = 0.0001f, x1;
        float denominator, cosx, cosval;
     
        // Converting degrees to radian
        n = n * (3.142f / 180.0f);
     
        x1 = 1;
     
        // Maps the sum along the series
        cosx = x1;
     
        // Holds the actual value of sin(n)
        cosval = (float)Math.cos(n);
        int i = 1;
        do {
            denominator = 2 * i * (2 * i - 1);
            x1 = -x1 * n * n / denominator;
            cosx = cosx + x1;
            i = i + 1;
        } while (accuracy <=
               Math.abs(cosval - cosx));
     
        return cosx;
    }
     
    // Function to find third side
    static float third_side(int a,
                    int b, float c)
    {
        float angle = cal_cos(c);
         
        return (float)Math.sqrt((a * a) +
            (b * b) - 2 * a * b * angle);
}
 
// Driver code
public static void main (String[] args)
{
    float c = 49;
    int a = 5, b = 8;
     
    // function call
    System.out.print(Math.round(third_side(a,
                    b, c)*100000.0)/100000.0);
}
}
 
// This code is contributed by Anant Agarwal.

Python3




# Python3 program to find third side
# of triangle using law of cosines
import math as mt
 
# Function to calculate cos
# value of angle c
def cal_cos(n):
 
    accuracy = 0.0001
    x1, denominator, cosx, cosval = 0, 0, 0, 0
 
    # Converting degrees to radian
    n = n * (3.142 / 180.0)
 
    x1 = 1
 
    # Maps the sum along the series
    cosx = x1
 
    # Holds the actual value of sin(n)
    cosval = mt.cos(n)
    i = 1
    while (accuracy <= abs(cosval - cosx)):
 
        denominator = 2 * i * (2 * i - 1)
        x1 = -x1 * n * n / denominator
        cosx = cosx + x1
        i = i + 1
 
    return cosx
 
# Function to find third side
def third_side(a, b, c):
    angle = cal_cos(c)
    return mt.sqrt((a * a) +
                   (b * b) - 2 * a * b * angle)
 
# Driver Code
c = 49
a, b = 5, 8
print(third_side(a, b, c))
 
# This code is contributed by mohit kumar

C#




// C# program to find third
// side of triangle using
// law of cosines
using System;
 
class GFG
{
    // Function to calculate
    // cos value of angle c
    static float cal_cos(float n)
    {
        float accuracy = 0.0001f, x1;
        float denominator, cosx, cosval;
     
        // Converting degrees to radian
        n = n * (3.142f / 180.0f);
     
        x1 = 1;
     
        // Maps the sum along the series
        cosx = x1;
     
        // Holds the actual value of sin(n)
        cosval = (float)Math.Cos(n);
        int i = 1;
        do {
            denominator = 2 * i * (2 * i - 1);
            x1 = -x1 * n * n / denominator;
            cosx = cosx + x1;
            i = i + 1;
        } while (accuracy <=
                Math.Abs(cosval - cosx));
     
        return cosx;
    }
     
    // Function to find third side
    static float third_side(int a,
                    int b, float c)
    {
        float angle = cal_cos(c);
         
        return (float)Math.Sqrt((a * a) +
               (b * b) - 2 * a * b * angle);
    }
 
    // Driver code
    public static void Main ()
    {
        float c = 49;
        int a = 5, b = 8;
         
        // function call
        Console.WriteLine(Math.Round(third_side(a,
                        b, c)*100000.0)/100000.0);
    }
}
 
// This code is contributed by vt_m.

PHP




<?php
// PHP program to find third
// side of triangle using
// law of cosines
 
// Function to calculate
// cos value of angle c
function cal_cos( $n )
{
    $accuracy = 0.0001;
    $x1; $denominator;
    $cosx; $cosval;
 
    // Converting degrees
    // to radian
    $n = $n * (3.142 / 180.0);
 
    $x1 = 1;
 
    // Maps the sum
    // along the series
    $cosx = $x1;
 
    // Holds the actual
    // value of sin(n)
    $cosval = cos($n);
    $i = 1;
    do
    {
        $denominator = 2 * $i *
                      (2 * $i - 1);
        $x1 = -$x1 * $n * $n /
               $denominator;
        $cosx = $cosx + $x1;
        $i = $i + 1;
    } while ($accuracy <= ($cosval -
                           $cosx));
 
    return $cosx;
}
 
// Function to find third side
function third_side($a, $b, $c)
{
    $angle = cal_cos($c);
    return sqrt(($a * $a) +
                ($b * $b) - 2 *
                 $a * $b * $angle);
}
 
// Driver Code
$c = 49;
$a = 5;
$b = 8;
 
// function call
echo third_side($a, $b, $c);
 
// This code is contributed
// by ajit
?>

Javascript




<script>
// Javascript program to find third
// side of triangle using
// law of cosines
 
    // Function to calculate
    // cos value of angle c
    function cal_cos( n) {
        let accuracy = 0.0001, x1;
        let denominator, cosx, cosval;
 
        // Converting degrees to radian
        n = n * (3.142 / 180.0);
 
        x1 = 1;
 
        // Maps the sum alet the series
        cosx = x1;
 
        // Holds the actual value of sin(n)
        cosval =  Math.cos(n);
        let i = 1;
        do {
            denominator = 2 * i * (2 * i - 1);
            x1 = -x1 * n * n / denominator;
            cosx = cosx + x1;
            i = i + 1;
        } while (accuracy <= Math.abs(cosval - cosx));
 
        return cosx;
    }
 
    // Function to find third side
    function third_side( a, b, c) {
        let angle = cal_cos(c);
 
        return  Math.sqrt((a * a) + (b * b) - 2 * a * b * angle);
    }
 
    // Driver code
      
        let c = 49;
        let a = 5, b = 8;
 
        // function call
        document.write(Math.round(third_side(a, b, c) * 100000.0) / 100000.0);
 
// This code is contributed by Rajput-Ji
</script>

Output: 
 

6.04339

 




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