# Length of diagonal of a parallelogram using adjacent sides and angle between them

Given two integers **a** and **b** where **a** and **b** represents the length of adjacent sides of a parallelogram and an angle between them, the task is to find the length of diagonal of the parallelogram.**0**

**Examples:**

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Input:a = 6, b = 10,~~0~~=30Output:6.14

Input:a = 3, b = 5,~~0~~=45Output:3.58

**Approach:** Consider a parallelogram **ABCD **with sides **a** and **b**, now apply cosine rule at angle **A **in the triangle **ABD **to find the length of diagonal **p**, similarly find diagonal **q **from triangle **ABC.**

Therefore the diagonals is given by:

## C++

`// C++ program to find length` `// Of diagonal of a parallelogram` `// Using sides and angle between them.` `#include <bits/stdc++.h>` `using` `namespace` `std;` `#define PI 3.147` `// Function to return the length` `// Of diagonal of a parallelogram` `// using sides and angle between them.` `double` `Length_Diagonal(` `int` `a, ` `int` `b, ` `double` `theta)` `{` ` ` `double` `diagonal = ` `sqrt` `((` `pow` `(a, 2) + ` `pow` `(b, 2)) -` ` ` `2 * a * b * ` `cos` `(theta * (PI / 180)));` ` ` `return` `diagonal;` `}` `// Driver Code` `int` `main()` `{` ` ` `// Given sides` ` ` `int` `a = 3;` ` ` `int` `b = 5;` ` ` `// Given angle` ` ` `double` `theta = 45;` ` ` `// Function call` ` ` `double` `ans = Length_Diagonal(a, b, theta);` ` ` `// Print the final answer` ` ` `printf` `(` `"%.2f"` `, ans);` `}` `// This code is contributed by Amit Katiyar` |

## Java

`// Java program to find length` `// Of diagonal of a parallelogram` `// Using sides and angle between them.` `class` `GFG{` `// Function to return the length` `// Of diagonal of a parallelogram` `// using sides and angle between them.` `static` `double` `Length_Diagonal(` `int` `a, ` `int` `b,` ` ` `double` `theta)` `{` ` ` `double` `diagonal = Math.sqrt((Math.pow(a, ` `2` `) +` ` ` `Math.pow(b, ` `2` `)) -` ` ` `2` `* a * b *` ` ` `Math.cos(theta *` ` ` `(Math.PI / ` `180` `)));` ` ` `return` `diagonal;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` ` ` `// Given sides` ` ` `int` `a = ` `3` `;` ` ` `int` `b = ` `5` `;` ` ` `// Given angle` ` ` `double` `theta = ` `45` `;` ` ` `// Function call` ` ` `double` `ans = Length_Diagonal(a, b, theta);` ` ` `// Print the final answer` ` ` `System.out.printf(` `"%.2f"` `, ans);` `}` `}` `// This code is contributed by amal kumar choubey` |

## Python3

`# Python3 Program to find length` `# Of diagonal of a parallelogram` `# Using sides and angle between them.` `import` `math ` ` ` `# Function to return the length` `# Of diagonal of a parallelogram` `# using sides and angle between them. ` `def` `Length_Diagonal(a, b, theta): ` ` ` ` ` `diagonal ` `=` `math.sqrt( ((a` `*` `*` `2` `) ` `+` `(b` `*` `*` `2` `))` ` ` `-` `2` `*` `a` `*` `b ` `*` `math.cos(math.radians(theta)))` ` ` ` ` `return` `diagonal ` ` ` `# Driver Code` `# Given Sides` `a ` `=` `3` `b ` `=` `5` `# Given Angle` `theta ` `=` `45` ` ` `# Function Call ` `ans ` `=` `Length_Diagonal(a, b, theta) ` ` ` `# Print the final answer` `print` `(` `round` `(ans, ` `2` `))` |

## C#

`// C# program to find length` `// Of diagonal of a parallelogram` `// Using sides and angle between them.` `using` `System;` `class` `GFG{` `// Function to return the length` `// Of diagonal of a parallelogram` `// using sides and angle between them.` `static` `double` `Length_Diagonal(` `int` `a, ` `int` `b,` ` ` `double` `theta)` `{` ` ` `double` `diagonal = Math.Sqrt((Math.Pow(a, 2) +` ` ` `Math.Pow(b, 2)) -` ` ` `2 * a * b *` ` ` `Math.Cos(theta *` ` ` `(Math.PI / 180)));` ` ` `return` `diagonal;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` ` ` `// Given sides` ` ` `int` `a = 3;` ` ` `int` `b = 5;` ` ` `// Given angle` ` ` `double` `theta = 45;` ` ` `// Function call` ` ` `double` `ans = Length_Diagonal(a, b, theta);` ` ` `// Print the readonly answer` ` ` `Console.Write(` `"{0:F2}"` `, ans);` `}` `}` `// This code is contributed by amal kumar choubey` |

## Javascript

`<script>` `// javascript program to find length` `// Of diagonal of a parallelogram` `// Using sides and angle between them.` `// Function to return the length` `// Of diagonal of a parallelogram` `// using sides and angle between them.` `function` `Length_Diagonal(a , b,theta)` `{` ` ` `var` `diagonal = Math.sqrt((Math.pow(a, 2) +` ` ` `Math.pow(b, 2)) -` ` ` `2 * a * b *` ` ` `Math.cos(theta *` ` ` `(Math.PI / 180)));` ` ` `return` `diagonal;` `}` `// Driver Code` `// Given sides` `var` `a = 3;` `var` `b = 5;` `// Given angle` `var` `theta = 45;` `// Function call` `var` `ans = Length_Diagonal(a, b, theta);` `// Print the final answer` `document.write(ans.toFixed(2));` `// This code is contributed by 29AjayKumar` `</script>` |

**Output:**

3.58

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