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 = 2
Output: 49.1
Explanation:
Area of triangle = 1 / 2 * (9 * 12 * Sin 2) = 35.12

Input: A = 2, B = 4, K = 1
Output: 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:

Area (ABC) = \frac{1}{2} \ A * B * sin(K)

Below is the implementation of the above approach:

C++

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// 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

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Java

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// 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

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Python3

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# 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)) 
  

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C#

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// 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

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Output:

49.1

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

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