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Area of Triangle using Side-Angle-Side (length of two sides and the included angle)
  • Last Updated : 07 Apr, 2021

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++




// 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);
 
// Prvar 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)
 

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