# Find the triangle area by using sas

The area of a triangle can be calculated using various methods, one of which is the Side-Angle-Side (SAS) method. In this method, you use two side lengths and the included angle to find the area of the triangle. The SAS method is particularly useful when you have the length of two sides and the angle between them and want to calculate the area of the triangle formed by those sides.

## Problem Statement

Given two side lengths (a and b) and the included angle (c) between them, the task is to calculate the area of the triangle using the SAS method. The formula for calculating the area of a triangle using the SAS method is:

Area = (a * b * sin(c)) / 2

## Example Scenario

Imagine you are working on a construction project and need to calculate the area of a triangular piece of land using the lengths of two sides and the angle between them. The SAS method would be ideal for this situation.

## Idea to Solve the Problem To solve this problem, you can follow these steps:

1. Accept the side lengths (a and b) and the included angle (c) in degrees as inputs.
2. Convert the angle from degrees to radians using the formula `radians = degrees * (M_PI / 180.0)`.
3. Use the provided formula to calculate the area of the triangle.
4. Display the calculated area.

## Pseudocode

``````function sas_triangle_area(a, b, c):
radians = c * (M_PI / 180.0)
area = (a * b * sin(radians)) / 2
return area

main:
a1, b1, c1 = 31.4, 29.3, 41
a2, b2, c2 = 17.9, 25.1, 98
a3, b3, c3 = 16.8, 33.6, 77

area1 = sas_triangle_area(a1, b1, c1)
area2 = sas_triangle_area(a2, b2, c2)
area3 = sas_triangle_area(a3, b3, c3)

print("Triangle [ Side a :", a1, "Side b :", b1, "Angle c :", c1, "]")
print("Area :", area1)

print("Triangle [ Side a :", a2, "Side b :", b2, "Angle c :", c2, "]")
print("Area :", area2)

print("Triangle [ Side a :", a3, "Side b :", b3, "Angle c :", c3, "]")
print("Area :", area3)``````

## Algorithm Explanation

1. Define a function `sas_triangle_area` that takes side lengths (a and b) and the included angle (c) as inputs.
2. Convert the angle from degrees to radians using the provided formula.
3. Calculate the area of the triangle using the SAS formula and return the result.
4. In the `main` function, set three test cases with different side lengths and angles.
5. Calculate the areas for each test case by calling the `sas_triangle_area` function.
6. Display the calculated areas along with their respective side lengths and angles.

## Code Solution

``````//C Program
//Find the area of sas triangle
#include <stdio.h>

#include <math.h>

//Find area of triangle using given sides a, b and angle c
void sas_triangle_area(double a, double b, int c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
double radians = c * (M_PI / 180.0);
double area = (a * b * sin(radians)) / 2;
printf(" Triangle  [ a : %lf, b : %lf c : %d ] ", a, b, c);
printf("\n Area : %lf\n\n", area);
}
int main()
{
//Test Cases
sas_triangle_area(31.4, 29.3, 41);
sas_triangle_area(17.9, 25.1, 98);
sas_triangle_area(16.8, 33.6, 77);
return 0;
}``````

#### Output

`````` Triangle  [ a : 31.400000, b : 29.300000 c : 41 ]
Area : 301.793714

Triangle  [ a : 17.900000, b : 25.100000 c : 98 ]
Area : 222.458770

Triangle  [ a : 16.800000, b : 33.600000 c : 77 ]
Area : 275.006207
``````
``````/*
Java program
Find the area of sas triangle
*/
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
public void sas_triangle_area(double a, double b, int c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
double radians = c * (Math.PI / 180.0);

double area = (a * b * Math.sin(radians)) / 2;

System.out.print(" Triangle [ a : " + a + ", b : " + b + " c : " + c + " ] ");
System.out.print("\n Area : " + area + "\n\n");
}
public static void main(String[] args)
{
TriangleArea obj = new TriangleArea();

obj.sas_triangle_area(31.4,29.3,41);

obj.sas_triangle_area(17.9,25.1,98);

obj.sas_triangle_area(16.8,33.6,77);
}
}``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.79371392592327

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245006

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.0062070849848
``````
``````/*
C++ program
Find the area of sas triangle
*/
#include<iostream>
#include<math.h>
using namespace std;
class TriangleArea
{
public:
//Find area of triangle using given sides a, b and angle c
void sas_triangle_area(double a, double b, int c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
double radians = c * (M_PI / 180.0);
double area = (a * b * sin(radians)) / 2;
cout << " Triangle [ a : " << a << ", b : " << b << " c : " << c << " ] ";
cout << "\n Area : " << area << "\n\n";
}
};
int main()
{
TriangleArea obj = TriangleArea();
obj.sas_triangle_area(31.4, 29.3, 41);
obj.sas_triangle_area(17.9, 25.1, 98);
obj.sas_triangle_area(16.8, 33.6, 77);
return 0;
}``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.794

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.459

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.006
``````
``````/*
C# program
Find the area of sas triangle
*/
using System;
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
public void sas_triangle_area(double a, double b, int c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
double radians = c * (Math.PI / 180.0);
double area = (a * b * Math.Sin(radians)) / 2;
Console.Write(" Triangle [ a : " + a + ", b : " + b + " c : " + c + " ] ");
Console.Write("\n Area : " + area + "\n\n");
}
public static void Main(String[] args)
{
TriangleArea obj = new TriangleArea();
obj.sas_triangle_area(31.4, 29.3, 41);
obj.sas_triangle_area(17.9, 25.1, 98);
obj.sas_triangle_area(16.8, 33.6, 77);
}
}``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.793713925923

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.006207084985
``````
``````<?php
/*
Php program
Find the area of sas triangle
*/
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
public	function sas_triangle_area(\$a, \$b, \$c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
\$radians = \$c * (M_PI / 180.0);
\$area = (\$a * \$b * sin(\$radians)) / 2;
echo " Triangle [ a : ". \$a .", b : ". \$b ." c : ". \$c ." ] ";
echo "\n Area : ". \$area ."\n\n";
}
}

function main()
{
\$obj = new TriangleArea();
\$obj->sas_triangle_area(31.4, 29.3, 41);
\$obj->sas_triangle_area(17.9, 25.1, 98);
\$obj->sas_triangle_area(16.8, 33.6, 77);
}
main();``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.79371392592

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.00620708498
``````
``````/*
Node Js program
Find the area of sas triangle
*/
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
sas_triangle_area(a, b, c)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
var radians = c * (Math.PI / 180.0);
var area = (a * b * Math.sin(radians)) / 2;
process.stdout.write(" Triangle [ a : " + a + ", b : " + b + " c : " + c + " ] ");
process.stdout.write("\n Area : " + area + "\n\n");
}
}

function main()
{
var obj = new TriangleArea();
obj.sas_triangle_area(31.4, 29.3, 41);
obj.sas_triangle_area(17.9, 25.1, 98);
obj.sas_triangle_area(16.8, 33.6, 77);
}
main();``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.79371392592327

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245006

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.0062070849848
``````
``````#   Python 3 program
#   Find the area of sas triangle
import math

class TriangleArea :
# Find area of triangle using given sides a, b and angle c
def sas_triangle_area(self, a, b, c) :
#  a and b is side
#  c is angle
#
# 	        Area of sas triangle
#
# 	              ab sin c
# 	            --------
# 	                2
#

#  Convert given degrees to radians
radians = c * (math.pi / 180.0)
area = (a * b * math.sin(radians)) / 2
print(" Triangle [ a : ", a ,", b : ", b ," c : ", c ," ] ", end = "")
print("\n Area : ", area ,"\n\n", end = "")

def main() :
obj = TriangleArea()
obj.sas_triangle_area(31.4, 29.3, 41)
obj.sas_triangle_area(17.9, 25.1, 98)
obj.sas_triangle_area(16.8, 33.6, 77)

if __name__ == "__main__": main()``````

#### Output

`````` Triangle [ a :  31.4 , b :  29.3  c :  41  ]
Area :  301.79371392592327

Triangle [ a :  17.9 , b :  25.1  c :  98  ]
Area :  222.45877030245006

Triangle [ a :  16.8 , b :  33.6  c :  77  ]
Area :  275.0062070849848
``````
``````#   Ruby program
#   Find the area of sas triangle

class TriangleArea

# Find area of triangle using given sides a, b and angle c
def sas_triangle_area(a, b, c)

#  a and b is side
#  c is angle
#
# 	        Area of sas triangle
#
# 	              ab sin c
# 	            --------
# 	                2
#

#  Convert given degrees to radians
radians = c * (Math::PI / 180.0)
area = (a * b * Math.sin(radians)) / 2
print(" Triangle [ a : ", a ,", b : ", b ," c : ", c ," ] ")
print("\n Area : ", area ,"\n\n")
end
end
def main()

obj = TriangleArea.new()
obj.sas_triangle_area(31.4, 29.3, 41)
obj.sas_triangle_area(17.9, 25.1, 98)
obj.sas_triangle_area(16.8, 33.6, 77)
end
main()``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.79371392592327

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245006

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.0062070849848

``````
``````/*
Scala program
Find the area of sas triangle
*/
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
def sas_triangle_area(a: Double, b: Double, c: Int): Unit = {
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
var radians: Double = c * (Math.PI / 180.0);
var area: Double = (a * b * Math.sin(radians)) / 2;
print(" Triangle [ a : " + a + ", b : " + b + " c : " + c + " ] ");
print("\n Area : " + area + "\n\n");
}
}
object Main
{
def main(args: Array[String]): Unit = {
var obj: TriangleArea = new TriangleArea();
obj.sas_triangle_area(31.4, 29.3, 41);
obj.sas_triangle_area(17.9, 25.1, 98);
obj.sas_triangle_area(16.8, 33.6, 77);
}
}``````

#### Output

`````` Triangle [ a : 31.4, b : 29.3 c : 41 ]
Area : 301.79371392592327

Triangle [ a : 17.9, b : 25.1 c : 98 ]
Area : 222.45877030245006

Triangle [ a : 16.8, b : 33.6 c : 77 ]
Area : 275.0062070849848
``````
``````/*
Swift program
Find the area of sas triangle
*/
import Foundation
class TriangleArea
{
//Find area of triangle using given sides a, b and angle c
func sas_triangle_area(_ a: Double, _ b: Double, _ c: Int)
{
// a and b is side
// c is angle
/*
Area of sas triangle

ab sin c
--------
2
*/
// Convert given degrees to radians
let radians: Double = Double(c) * (Double.pi / 180);
let area: Double = (a * b * sin(radians)) / 2;
print(" Triangle [ a : ", a ,", b : ", b ," c : ", c ," ] ", terminator: "");
print("\n Area : ", area ,"\n\n", terminator: "");
}
}
func main()
{
let obj: TriangleArea = TriangleArea();
obj.sas_triangle_area(31.4, 29.3, 41);
obj.sas_triangle_area(17.9, 25.1, 98);
obj.sas_triangle_area(16.8, 33.6, 77);
}
main();``````

#### Output

`````` Triangle [ a :  31.4 , b :  29.3  c :  41  ]
Area :  301.793713925923

Triangle [ a :  17.9 , b :  25.1  c :  98  ]
Area :  222.45877030245

Triangle [ a :  16.8 , b :  33.6  c :  77  ]
Area :  275.006207084985
``````

## Output Explanation

The code calculates the area for each test case using the SAS method and displays the results. For a triangle with side lengths (a, b) = (31.4, 29.3) and included angle (c) = 41, the area is approximately 301.793714. Similarly, for other test cases, the areas are calculated and displayed.

## Time Complexity

The time complexity of this code is constant O(1) because the calculations involve basic arithmetic and trigonometric operations (sin) that are computed in constant time regardless of the input size. The program performs a fixed number of operations for each test case, making it efficient.

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