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

• Last Updated : 08 Apr, 2021

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

Examples:

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

Input: a = 3, b = 5, 0=45
Output: 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 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 Codeint 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 Codepublic 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 Sidesa = 3b = 5 # Given Angletheta = 45   # Function Call ans = Length_Diagonal(a, b, theta)    # Print the final answerprint(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 Codepublic 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

 
Output:
3.58

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

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