Given two integers **A** and **theta**, denoting the length of a side of a rhombus and the vertex angle respectively, the task is to find the length of the diagonals of the rhombus.

**Examples:**

Input:A = 10, theta = 30Output:19.32 5.18

Input:A = 6, theta = 45Output:11.09 4.59

**Approach:**

The problem can be solved using the law of cosines. Using the **law of cosines** on triangles formed by the diagonals and sides of the rhombus gives the following relation to calculate the length of diagonals:

Below is the implementation of the above approach:

## C++

`// C++ program to implement` `// the above approach` `#include <bits/stdc++.h>` `using` `namespace` `std;` `// Function to calculate the length` `// of diagonals of a rhombus using` `// length of sides and vertex angle` `double` `Length_Diagonals(` `int` `a, ` `double` `theta)` `{` ` ` `double` `p = a * ` `sqrt` `(2 + (2 * ` `cos` `(` ` ` `theta * (3.141 / 180))));` ` ` `double` `q = a * ` `sqrt` `(2 - (2 * ` `cos` `(` ` ` `theta * (3.141 / 180))));` ` ` ` ` `cout << fixed << setprecision(2) << p` ` ` `<< ` `" "` `<< q;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `a = 6;` ` ` `int` `theta = 45;` ` ` ` ` `// Function Call` ` ` `Length_Diagonals(a, theta);` ` ` ` ` `return` `0;` `}` `// This code is contributed by Virusbuddah_` |

## Java

`// Java program to implement` `// the above approach` `class` `GFG{` `// Function to calculate the length` `// of diagonals of a rhombus using` `// length of sides and vertex angle` `static` `double` `[] Length_Diagonals(` `int` `a, ` `double` `theta)` `{` ` ` `double` `p = a * Math.sqrt(` `2` `+ (` `2` `*` ` ` `Math.cos(theta * (Math.PI / ` `180` `))));` ` ` `double` `q = a * Math.sqrt(` `2` `- (` `2` `*` ` ` `Math.cos(theta * (Math.PI / ` `180` `))));` ` ` `return` `new` `double` `[]{ p, q };` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `A = ` `6` `;` ` ` `double` `theta = ` `45` `;` ` ` ` ` `double` `[] ans = Length_Diagonals(A, theta);` ` ` `System.out.printf(` `"%.2f"` `+ ` `" "` `+ ` `"%.2f"` `,` ` ` `ans[` `0` `], ans[` `1` `]);` `}` `}` `// This code is contributed by Princi Singh` |

## Python3

`# Python Program to implement` `# the above approach` `import` `math` `# Function to calculate the length` `# of diagonals of a rhombus using` `# length of sides and vertex angle` `def` `Length_Diagonals(a, theta):` ` ` `p ` `=` `a ` `*` `math.sqrt(` `2` `+` `(` `2` `*` `\` ` ` `math.cos(math.radians(theta))))` ` ` ` ` `q ` `=` `a ` `*` `math.sqrt(` `2` `-` `(` `2` `*` `\` ` ` `math.cos(math.radians(theta))))` ` ` `return` `[p, q]` `# Driver Code` `A ` `=` `6` `theta ` `=` `45` `ans ` `=` `Length_Diagonals(A, theta)` `print` `(` `round` `(ans[` `0` `], ` `2` `), ` `round` `(ans[` `1` `], ` `2` `))` |

## C#

`// C# program to implement` `// the above approach` `using` `System;` `class` `GFG{` `// Function to calculate the length` `// of diagonals of a rhombus using` `// length of sides and vertex angle` `static` `double` `[] Length_Diagonals(` `int` `a, ` `double` `theta)` `{` ` ` `double` `p = a * Math.Sqrt(2 + (2 *` ` ` `Math.Cos(theta * (Math.PI / 180))));` ` ` `double` `q = a * Math.Sqrt(2 - (2 *` ` ` `Math.Cos(theta * (Math.PI / 180))));` ` ` `return` `new` `double` `[]{ p, q };` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `A = 6;` ` ` `double` `theta = 45;` ` ` ` ` `double` `[] ans = Length_Diagonals(A, theta);` ` ` `Console.Write(` `"{0:F2}"` `+ ` `" "` `+ ` `"{1:F2}"` `,` ` ` `ans[0], ans[1]);` `}` `}` `// This code is contributed by gauravrajput1` |

## Javascript

`<script>` `// JavaScript program for the above approach` `// Function to calculate the length` `// of diagonals of a rhombus using` `// length of sides and vertex angle` `function` `Length_Diagonals(a, theta)` `{` ` ` `let p = a * Math.sqrt(2 + (2 *` ` ` `Math.cos(theta * (Math.PI / 180))));` ` ` ` ` `let q = a * Math.sqrt(2 - (2 *` ` ` `Math.cos(theta * (Math.PI / 180))));` ` ` ` ` `return` `[ p, q ];` `}` ` ` `// Driver Code` ` ` ` ` `let A = 6;` ` ` `let theta = 45;` ` ` ` ` `let ans = Length_Diagonals(A, theta);` ` ` ` ` `document.write(ans[0].toFixed(2) + ` `" "` ` ` `+ ans[1].toFixed(2));` ` ` `</script>` |

**Output:**

11.09 4.59

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

Attention reader! Don’t stop learning now. Get hold of all the important DSA concepts with the **DSA Self Paced Course** at a student-friendly price and become industry ready. To complete your preparation from learning a language to DS Algo and many more, please refer **Complete Interview Preparation Course****.**

In case you wish to attend live classes with industry experts, please refer **DSA Live Classes**