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Length of remaining two sides of a Triangle from a given side and its adjacent angles

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  • Last Updated : 28 Jan, 2022

Given the length of a side a of a triangle and its adjacent angles B and C, the task is to find the remaining two sides of the triangle. 

Input: a = 5, B = 62.2, C = 33.5 
Output: 4.44, 2.77 
Explanation 
The remaining two sides of the triangle are b = 4.44488228556699 and c = 2.7733977979419038
Input: a = 12, B = 60, C = 30 
Output: 10.39, 5.99 
Explanation 
The remaining two sides of the triangle are b = 10.392304845413264 and c = 5.999999999999999 
 

Approach:  

  1. The remaining angle can be calculated by the angle sum theorem in a triangle:
  2. The other two sides of triangle can be computed using sine formula:

Below is the implementation of the above approach: 
 

C++




// C++ program for above approach
#include<bits/stdc++.h>
using namespace std;
 
// Function for computing other
// 2 side of the triangle
void findSide(float a, float B, float C)
{
     
    // Computing angle C
    float A = 180 - C - B;
     
    // Converting A in to radian
    float radA = M_PI * (A / 180);
     
    // Converting B in to radian
    float radB = M_PI * (B / 180);
     
    // Converting C in to radian
    float radC = M_PI * (C / 180);
     
    // Computing length of side b
    float b = a / sin(radA) * sin(radB);
     
    // Computing length of side c
    float c = a / sin(radA) * sin(radC);
     
    cout << fixed << setprecision(15) << b << " ";
    cout << fixed << setprecision(15) << c;
}
 
// Driver code
int main()
{
    int a = 12, B = 60, C = 30;
     
    // Calling function
    findSide(a, B, C);
}
 
// This code is contributed by ishayadav181

Java




// Java program for above approach
import java.util.*;
 
class GFG{
 
// Function for computing other
// 2 side of the triangle
static void findSide(double a, double B,
                     double C)
{
     
    // Computing angle C
    double A = 180 - C - B;
     
    // Converting A in to radian
    double radA = (Math.PI * (A / 180));
     
    // Converting B in to radian
    double radB = (Math.PI * (B / 180));
     
    // Converting C in to radian
    double radC = (Math.PI * (C / 180));
     
    // Computing length of side b
    double b = (a / Math.sin(radA) *
                    Math.sin(radB));
     
    // Computing length of side c
    double c = (a / Math.sin(radA) *
                    Math.sin(radC));
     
    System.out.printf("%.15f", b);
    System.out.printf(" %.15f", c);
}
 
// Driver code
public static void main(String[] args)
{
    int a = 12, B = 60, C = 30;
     
    // Calling function
    findSide(a, B, C);
}
}
 
// This code is contributed by Amit Katiyar

Python3




# Python3 program for above approach
import math
 
# Function for computing other
# 2 side of the triangle
def findSide(a, B, C):
 
    # computing angle C
    A = 180-C-B
 
    # converting A in to radian
    radA = math.pi *(A / 180)
 
    # converting B in to radian
    radB = math.pi *(B / 180)
 
    # converting C in to radian
    radC = math.pi *(C / 180)
 
    # computing length of side b
    b = a / math.sin(radA)*math.sin(radB)
 
    # computing length of side c
    c = a / math.sin(radA)*math.sin(radC)
 
    return b, c
 
# driver program
a = 12
B = 60
C = 30
 
# calling function
b, c = findSide(a, B, C)
print(b, c)

C#




// C# program for above approach
using System;
class GFG{
 
// Function for computing other
// 2 side of the triangle
static void findSide(float a,
                     double B, double C)
{   
  // Computing angle C
  double A = 180 - C - B;
 
  // Converting A in to radian
  double radA = (Math.PI * (A / 180));
 
  // Converting B in to radian
  double radB = (Math.PI * (B / 180));
 
  // Converting C in to radian
  double radC = (Math.PI * (C / 180));
 
  // Computing length of side b
  double b = (a / Math.Sin(radA) *
              Math.Sin(radB));
 
  // Computing length of side c
  double c = (a / Math.Sin(radA) *
              Math.Sin(radC));
 
  Console.Write("{0:F15}", b);
  Console.Write("{0:F15}", c);
}
 
  // Driver code
  public static void Main(String[] args)
  {
    int a = 12, B = 60, C = 30;
 
    // Calling function
    findSide(a, B, C);
  }
}
 
// This code is contributed by 29AjayKumar

Javascript




<script>
// Javascript program for above approach
 
// Function for computing other
// 2 side of the triangle
function findSide(a, B, C)
{
     
    // Computing angle C
    var A = 180 - C - B;
     
    // Converting A in to radian
    var radA = Math.PI * (A / 180);
     
    // Converting B in to radian
    var radB = Math.PI * (B / 180);
     
    // Converting C in to radian
    var radC = Math.PI * (C / 180);
     
    // Computing length of side b
    var b = a / Math.sin(radA) * Math.sin(radB);
     
    // Computing length of side c
    var c = a / Math.sin(radA) * Math.sin(radC);
     
    document.write( b + " ");
    document.write( c);
}
 
// Driver code
var a = 12, B = 60, C = 30;
 
// Calling function
findSide(a, B, C);
 
</script>

Output: 

10.392304845413264 5.999999999999999

 

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


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