# Area of Triangle using Side-Angle-Side (length of two sides and the included angle)

Given two integers **A**, **B** representing the length of two sides of a triangle and an integer **K **representing the angle between them in radian, the task is to calculate the area of the triangle from the given information.**Examples:**

Input:a = 9, b = 12, K = 2Output:49.1Explanation:

Area of triangle = 1 / 2 * (9 * 12 * Sin 2) = 35.12Input:A = 2, B = 4, K = 1Output:3.37

**Approach:**

Consider the following triangle **ABC** with sides **A**, **B**, **C**, and an angle **K** between sides **A** and** B**.

Then, the area of the triangle can be calculated using the Side-Angle-Side formula:

Below is the implementation of the above approach:

## C++

`// C++ program to calculate` `// the area of a triangle when` `// the length of two adjacent` `// sides and the angle between` `// them is provided` `#include <bits/stdc++.h>` `using` `namespace` `std;` `float` `Area_of_Triangle(` `int` `a, ` `int` `b, ` `int` `k)` `{` ` ` `float` `area = (` `float` `)((1 / 2.0) *` ` ` `a * b * (` `sin` `(k)));` ` ` `return` `area;` `}` `// Driver Code` `int` `main()` `{` ` ` `int` `a = 9;` ` ` `int` `b = 12;` ` ` `int` `k = 2;` ` ` `// Function Call` ` ` `float` `ans = Area_of_Triangle(a, b, k);` ` ` `// Print the final answer` ` ` `cout << ans << endl;` `}` `// This code is contributed by Ritik Bansal` |

## Java

`// Java program to calculate` `// the area of a triangle when` `// the length of two adjacent` `// sides and the angle between` `// them is provided` `class` `GFG{` `// Function to return the area of` `// triangle using Side-Angle-Side` `// formula` `static` `float` `Area_of_Triangle(` `int` `a, ` `int` `b,` ` ` `int` `k)` `{` ` ` `float` `area = (` `float` `)((` `1` `/ ` `2.0` `) *` ` ` `a * b * Math.sin(k));` ` ` `return` `area;` `}` `// Driver Code` `public` `static` `void` `main(String[] args)` `{` ` ` `int` `a = ` `9` `;` ` ` `int` `b = ` `12` `;` ` ` `int` `k = ` `2` `;` ` ` `// Function Call` ` ` `float` `ans = Area_of_Triangle(a, b, k);` ` ` `// Print the final answer` ` ` `System.out.printf(` `"%.1f"` `,ans);` `}` `}` `// This code is contributed by sapnasingh4991` |

## Python3

`# Python3 program to calculate` `# the area of a triangle when` `# the length of two adjacent` `# sides and the angle between` `# them is provided` `import` `math` `# Function to return the area of` `# triangle using Side-Angle-Side` `# formula` `def` `Area_of_Triangle(a, b, k):` ` ` `area ` `=` `(` `1` `/` `2` `) ` `*` `a ` `*` `b ` `*` `math.sin(k)` ` ` `return` `area` `# Driver Code` `a ` `=` `9` `b ` `=` `12` `k ` `=` `2` `# Function Call` `ans ` `=` `Area_of_Triangle(a, b, k)` `# Print the final answer` `print` `(` `round` `(ans, ` `2` `))` |

## C#

`// C# program to calculate` `// the area of a triangle when` `// the length of two adjacent` `// sides and the angle between` `// them is provided` `using` `System;` `class` `GFG{` `// Function to return the area of` `// triangle using Side-Angle-Side` `// formula` `static` `float` `Area_of_Triangle(` `int` `a, ` `int` `b,` ` ` `int` `k)` `{` ` ` `float` `area = (` `float` `)((1 / 2.0) *` ` ` `a * b * Math.Sin(k));` ` ` `return` `area;` `}` `// Driver Code` `public` `static` `void` `Main(String[] args)` `{` ` ` `int` `a = 9;` ` ` `int` `b = 12;` ` ` `int` `k = 2;` ` ` `// Function Call` ` ` `float` `ans = Area_of_Triangle(a, b, k);` ` ` `// Print the readonly answer` ` ` `Console.Write(` `"{0:F1}"` `, ans);` `}` `}` `// This code is contributed by sapnasingh4991` |

## Javascript

`<script>` `// javascript program to calculate` `// the area of a triangle when` `// the length of two adjacent` `// sides and the angle between` `// them is provided// Function to return the area of` `// triangle using Side-Angle-Side` `// formula` `function` `Area_of_Triangle(a , b, k)` `{` ` ` `var` `area = ((1 / 2.0) *` ` ` `a * b * Math.sin(k));` ` ` `return` `area;` `}` `// Driver Code` `var` `a = 9;` `var` `b = 12;` `var` `k = 2;` `// Function Call` `var` `ans = Area_of_Triangle(a, b, k);` `// Print the final answer` `document.write(ans.toFixed(1));` `// This code is contributed by 29AjayKumar` `</script>` |

**Output:**

49.1

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