Question

Write a C++ program to analyze a variety of triangles. The program should determine all angles and all sides for a triangle for three different options (give the user a menu of choices):

Given two angles and one side

First check to be sure that the three values entered are valid. In particular, the following conditions must be met:

• Side > 0
• For each angle: 0 < angle < 180 (if angle is in radians, convert it to degrees first and then check)
• For the sum of the two angles entered: 0 < Sum < 180 (if angles are in radians, convert them to degrees first and then check)

Example 2:
If A = 30°, B = 100°, and a = 20, then
Find the remaining angle:
C = 180 - 30 - 100 = 50°
Find the two remaining sides using the law of sines:
sinAa = sinBb = sinCc
sin30°20 = sin100°b= sin50°c
so   b = a⋅sin(B)sin(A) = 20sin(100°)sin(30°) = 39.39
and c = a⋅sin(C)sin(A) = 20sin(50°)sin(30°) = 30.6

Answer 1

#include <iostream>
#include <cmath>

using namespace std;

int main()
{
//variables
float aside, bside, cside;
float aangle,bangle,cangle;
  
//enter side a
while(1){
cout<<"enter the length of side a "<<endl;
cin>>aside;
  
if(aside > 0)
break;
}
  
//enter the angle
while(1){
cout<<"enter the first angle "<<endl;
cin>>aangle;

if( (aangle > 0) && (aangle < 180))
break;
}
  
  
while(1){
cout<<"enter the Second angle "<<endl;
cin>>bangle;


if( (bangle > 0) && (bangle < 180))
break;

}
  
cangle = 180 - aangle - bangle;
  
  
bside = (aside * sin(bangle)) / sin(aangle);
cside = (aside * sin(cangle)) / sin(aangle);

cout << "Side 1 "<< aside << endl;
cout << "Angle 1 "<< aangle << endl;
cout << "Side 2 "<< bside << endl;
cout << "Angle 2 "<< bangle << endl;
cout << "Side 3 "<< cside << endl;
cout << "Angle 3 "<< cangle << endl;

return 0;
}