C Program To Check Triangle By Entering 3 Angles Of A Triangle

When working with geometric shapes, understanding their fundamental properties is crucial. Triangles, being the simplest polygons, have specific rules governing their angles. In this article, you will learn how to write a C program to determine if three given angles can form a valid triangle.

Problem Statement

The core problem is to validate whether three numerical inputs, representing angles, can constitute a real-world triangle. This requires adhering to two fundamental geometric principles: the sum of the interior angles of any triangle must precisely equal 180 degrees, and each individual angle must be greater than zero. Failing either of these conditions means the angles cannot form a valid triangle.

Example

Consider the following input and expected output scenarios for validating triangle angles:

Input: Angle 1: 60 Angle 2: 70 Angle 3: 50

Expected Output: The angles 60, 70, and 50 form a valid triangle.

Background & Knowledge Prerequisites

To understand and implement the solution, a basic grasp of the following C programming concepts is essential:

• Variable Declaration: How to declare integer variables (e.g., int angle1;).
• Input/Output Operations: Using printf() for displaying output and scanf() for reading user input.
• Arithmetic Operators: Performing addition (+).
• Relational Operators: Comparing values (e.g., == for equality, > for greater than).
• Logical Operators: Combining conditions (e.g., && for logical AND).
• Conditional Statements: Using if-else statements to execute code blocks based on conditions.

Use Cases or Case Studies

Validating triangle angles is a fundamental operation with several practical applications:

• Educational Software: Programs designed to teach geometry can use this logic to check user-entered angle values for triangle construction.
• CAD and Design Tools: In computer-aided design, ensuring geometric validity is critical when users define shapes or models, preventing the creation of impossible structures.
• Game Development: For level design or physics engines, verifying the geometry of triangular meshes (common in 3D graphics) ensures shapes are correctly formed.
• Surveying and Mapping: When calculating areas or distances based on triangular plots of land, initial validation of measured angles prevents errors in subsequent computations.
• Scientific Simulations: In simulations involving forces or structures, ensuring the stability and validity of triangular components is a prerequisite for accurate modeling.

Solution Approaches

For validating triangle angles, the most direct and efficient approach involves a single conditional check based on the two fundamental geometric rules.

Approach 1: Direct Conditional Validation

This approach directly checks if the sum of the three angles is 180 and if each angle is positive using a single if statement.

One-line summary: Read three angles from the user and verify if their sum is 180 degrees and each angle is positive.

Code example:

// Triangle Angle Validator
#include <stdio.h>

int main() {
    // Step 1: Declare variables for the three angles
    int angle1, angle2, angle3;

    // Step 2: Prompt user to enter the angles
    printf("Enter the first angle: ");
    scanf("%d", &angle1);

    printf("Enter the second angle: ");
    scanf("%d", &angle2);

    printf("Enter the third angle: ");
    scanf("%d", &angle3);

    // Step 3: Check conditions for a valid triangle
    // Condition 1: Sum of angles must be 180
    // Condition 2: Each angle must be greater than 0
    if (angle1 > 0 && angle2 > 0 && angle3 > 0 && (angle1 + angle2 + angle3 == 180)) {
        printf("The angles %d, %d, and %d form a valid triangle.\\n", angle1, angle2, angle3);
    } else {
        printf("The angles %d, %d, and %d do NOT form a valid triangle.\\n", angle1, angle2, angle3);
    }

    return 0;
}

Run

Sample output:

Enter the first angle: 60
Enter the second angle: 70
Enter the third angle: 50
The angles 60, 70, and 50 form a valid triangle.

Enter the first angle: 90
Enter the second angle: 90
Enter the third angle: 10
The angles 90, 90, and 10 do NOT form a valid triangle.

Enter the first angle: -10
Enter the second angle: 90
Enter the third angle: 100
The angles -10, 90, and 100 do NOT form a valid triangle.

Stepwise explanation for clarity:

1. Include Header: The #include line includes the standard input/output library, necessary for printf and scanf.
2. Main Function: The program execution begins in the main() function.
3. Variable Declaration: Three integer variables, angle1, angle2, and angle3, are declared to store the user's input.
4. User Input: The program prompts the user to enter each angle using printf() and then reads the integer values into the respective variables using scanf(). The %d format specifier is used for reading integers.
5. Validation Logic: An if statement contains the core validation logic:

• angle1 > 0 && angle2 > 0 && angle3 > 0: This part checks if each angle is positive. A triangle cannot have zero or negative angles.
• (angle1 + angle2 + angle3 == 180): This part checks if the sum of all three angles is exactly 180 degrees.
• The && (logical AND) operator ensures that *all* conditions must be true for the angles to form a valid triangle.

1. Output:

• If all conditions in the if statement are met, a message indicating a valid triangle is printed.
• Otherwise, the else block executes, and a message indicating an invalid triangle is displayed.

1. Return 0: The return 0; statement indicates successful program execution.

Conclusion

Validating whether three angles form a valid triangle is a foundational problem in geometry, directly tied to the geometric principles that the sum of angles must be 180 degrees and each angle must be positive. By implementing a straightforward conditional check in C, we can efficiently determine the validity of any given set of angles. This simple program demonstrates the power of conditional logic and basic arithmetic in solving practical problems.

Summary

• A valid triangle requires three angles.
• The sum of these three angles must be exactly 180 degrees.
• Each individual angle must be greater than 0 degrees.
• C programming's if-else statements combined with logical and arithmetic operators provide an effective way to implement this validation.
• Such validation is crucial in various applications, from educational tools to advanced design software.