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):

1. Given two sides and the angle between
2. Given two angles and one side
3. Given three sides

Option 1: Given two sides and the angle between

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

• Both sides > 0
• If angle is in degrees, then 0 < angle < 180 (if angle is in radians, convert it to degrees first and then check)

Option 2: 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)

Other program requirements:

• The user should be able to indicate whether and angle is being entered is in degrees or in radians by entering either d or D for degrees or entering r or R for radians. Examples:
  • Please enter the angle: 30 d
  • Please enter the angle: 30 D
  • Please enter the angle: 1.5 r
  • Please enter the angle: 1.5 R
• If any bad inputs are entered, print out an appropriate error message and terminate the program using the command: return 1;

Bad inputs include invalid triangles, invalid menu choices, and invalid units for angles.

• Example:

if (Side < 0)

{ cout << Error. Negative value for side not allowed. Program terminated.;

Return 1;

}

• After performing the calculations for any of the three menu choices, display the values for all three sides and all three angles (in degrees).
  • Use 2 digits after the decimal pint for all angles.
  • Use 3 digits after the decimal pint for all sides.
  • Include the unit degrees after all angles.
  • N units are required for the sides.
• Note that for option 2, the calculations are different based on which side is entered. Ask the user to enter angles A and B, and then ask the user which side that they would like to enter (a, b, or c). Perform the appropriate calculations in each case.
• Run the program for the following 7 test cases:
  • Optin 1: a = 20, b = 15, C = 35
  • Optin 1: a = 20, b = 15, C = 0.5 radians
  • Optin 2: A = 30, B = 100, and a = 20
  • Optin 2: A = 30, B = 100, and b = 20\
  • Optin 2: A = 30, B = 100, and c = 20
  • Optin 3: a = 20, b = 15, c = 10\
  • Optin 3: a = 5, b = 12, c = 13