Question

Write a program that reads three nonzero double values and determines and prints whether they could represent the sides of a triangle.

Short answer

The sides form a triangle if they satisfy the triangle inequality theorem.

Step-by-step solution

Understand Triangle Inequality Theorem

The triangle inequality theorem states that for three sides to form a triangle, the sum of the lengths of any two sides must be greater than the length of the third side. Thus, for sides a, b, and c, the conditions are: \( a + b > c \), \( a + c > b \), and \( b + c > a \).

Define the Triangle Function

Create a function named `is_triangle` that takes three parameters. These parameters will represent the lengths of the three sides.

Implement Logical Conditions

Within the `is_triangle` function, use conditional statements to check if all three conditions of the triangle inequality theorem are satisfied.

Return the Result

If all three conditions are true, print a message that the sides can form a triangle. Otherwise, print a message indicating they cannot.

Obtain User Input

Ask the user to input three nonzero double values. Make sure to convert these values from strings to floats.

Invoke the Function with User Input

Pass the input values to the `is_triangle` function and execute the program to display the result.

Code Implementation

Here's an example of how the program might look in Python: ```python def is_triangle(a, b, c): if a + b > c and a + c > b and b + c > a: print('The sides can form a triangle.') else: print('The sides cannot form a triangle.') # Taking input from the user a = float(input('Enter the first side: ')) b = float(input('Enter the second side: ')) c = float(input('Enter the third side: ')) # Check if it's a triangle is_triangle(a, b, c) ```

Key concepts

Conditional Statements

Conditional statements are an essential part of programming that allow us to make decisions based on certain conditions. In the context of determining whether three sides can form a triangle, conditional statements evaluate whether the Triangle Inequality Theorem is met.
The basic structure of a conditional statement includes an `if` keyword, followed by a condition in parentheses. If this condition is true, the code block under the `if` statement executes. If false, any code under an `else` or `elif` (else-if) block executes.
For instance, in checking if sides can form a triangle, you’d use:

• `if a + b > c`: checks if the sum of sides `a` and `b` is greater than `c`.
• `and a + c > b`: further checks if `a` and `c` together are greater than `b`.
• `and b + c > a`: also ensures `b` and `c` together exceed `a`.

When you chain conditions with `and`, all conditions must be true for the overall statement to be true. This logical structure helps in making precise decisions, like determining valid triangle side lengths.

User Input

User input is vital when creating interactive programs, like the one designed to check for triangle possibilities. Here, the program requires users to input three nonzero double values representing potential sides of a triangle. This process turns the program dynamic, as it processes different inputs each time it's run.
In Python, taking user input is achieved using the `input()` function which reads the input as a string. Since computations need numerical values, these string inputs need conversion to floats. This is handled by wrapping the `input()` call with the `float()` function.
For instance:

• `a = float(input('Enter the first side: '))`: captures and converts the user input for the first side.
• `b = float(input('Enter the second side: '))`: does the same for the second side.
• `c = float(input('Enter the third side: '))`: processes the third side.

This simple interaction makes the program user-friendly and adaptable to varied inputs, ensuring that the calculations are always based on fresh, user-provided data.

Function Definition

Defining functions is an integral part of programming, allowing for code reusability and organization. In this context, a function named `is_triangle` is defined to encapsulate the logic that determines if the given side lengths can form a triangle.
Functions are created using the `def` keyword, followed by the function name and parameters in parentheses. For the triangle check, `is_triangle` takes three parameters—`a`, `b`, and `c`, representing side lengths.
Inside the function, encapsulated logic pertains to the Triangle Inequality Theorem, using conditional statements. Once defined, the function can be called whenever needed:

• `is_triangle(a, b, c)`: Here, `a`, `b`, and `c` are input values passed to the function. It executes the embedded triangle-check logic within its scope.
• This separation via function enhances clarity and reusability. Functions can be tested independently or called multiple times in a program with varying inputs.

Using functions effectively streamlines complex programs and aids in maintaining organized, readable code.

Logical Conditions

Logical conditions form the backbone of decision-making in programming. They enable the program to execute specific blocks of code based on whether conditions are true or false. In determining if three sides can form a triangle, logical conditions from the Triangle Inequality Theorem are pivotal.
A logical condition involves operators like `>`, `<`, `==`, and logical connectors such as `and`, `or`, and `not`. In our triangle scenario, the `and` operator stringently checks multiple conditions altogether.
The Triangle Inequality conditions are implemented as:

• `a + b > c`
• `a + c > b`
• `b + c > a`

All these must be `True` simultaneously for `is_triangle` to ascertain that the sides form a valid triangle.
Utilizing logical conditions correctly ensures that programs execute intended operations, allowing for versatile, condition-based responses in code. Every logical condition checked is a step towards the required computational decision.