# Program to find third side of triangle using law of cosines

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
```

## Recommended: Please try your approach on {IDE} first, before moving on to the solution.

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 ` `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. `

/div>

## 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

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 [tabby title="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

 ` `

Output:

```6.04339
```