Program to find third side of triangle using law of cosines

08 Jun, 2022
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 
 
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++
Java
Python3
C#
PHP
Javascript
// 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 cfloat 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 sidefloat 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 functionint main(){    float c = 49;    int a = 5, b = 8;    // function call    cout << third_side(a, b, c);     return 0;}
// Java program to find third// side of triangle using// law of cosinesclass 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 codepublic 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 program to find third side# of triangle using law of cosinesimport math as mt # Function to calculate cos# value of angle cdef 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 sidedef third_side(a, b, c):    angle = cal_cos(c)    return mt.sqrt((a * a) +                   (b * b) - 2 * a * b * angle) # Driver Codec = 49a, b = 5, 8print(third_side(a, b, c)) # This code is contributed by mohit kumar
// C# program to find third// side of triangle using// law of cosinesusing 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 program to find third// side of triangle using// law of cosines // Function to calculate// cos value of angle cfunction 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 $cosx;} // Function to find third sidefunction third_side($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 callecho third_side($a, $b, $c); // This code is contributed// by ajit?>
<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>
6.04339
Time Complexity: O(1), as the loop for calculating cosine value is limited by a period and so it runs a finite amount of time Auxiliary Space: O(1), as we are not using any extra space.
jit_t
mohit kumar 29
Rajput-Ji
rohitsingh57
triangle
Geometric
School Programming
Geometric
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