Question

Write an application that reads three nonzero integers and determines and prints whether they could represent the sides of a right triangle.

Short answer

Read and sort the three integers, apply the Pythagorean theorem and print whether they form a right triangle or not.

Step-by-step solution

Understanding the Problem

The application needs to determine if three nonzero integers can be the sides of a right triangle. By the Pythagorean theorem, this is true if the squares of the two smaller numbers add up to the square of the largest number.

Input Read and Sort

Read three nonzero integer values from the user. Sort the numbers in non-descending order so you can identify the hypotenuse (the largest number) and the other two sides.

Apply Pythagorean Theorem

Calculate the squares of the three numbers. Check if the sum of the squares of the two smaller numbers is equal to the square of the largest number. If so, they can form a right triangle.

Output the Result

Print whether the given integers can form the sides of a right triangle based on the result of the Pythagorean theorem check.

Key concepts

Right Triangle Determination

Identifying a right triangle is a fundamental aspect of geometry, often visualized as a triangle with one angle measuring exactly 90 degrees. One of the most reliable methods of determining whether a set of three sides can form a right triangle is by utilizing the Pythagorean theorem, which applies exclusively to right-angled triangles.

The rule for the Pythagorean theorem is simple: in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides. This can be expressed in the equation \( a^2 + b^2 = c^2 \), where \( c \) represents the hypotenuse and \( a \) and \( b \) are the other two sides.

A practical exercise to solidify this concept would involve using real-life scenarios where right triangles commonly occur, such as in construction or computer graphics. By measuring and calculating with real objects, learners can better understand the application of the Pythagorean theorem to physical structures and models.

Programming Logic for Mathematical Concepts

Translating mathematical concepts into programming logic is a crucial skill in computer science. When working with geometric problems like the Pythagorean theorem, programmers need to design an algorithm—that is, a step-by-step procedure—to verify geometric conditions.

Let's consider the Pythagorean theorem application as our example. The programming logic must first ensure all provided sides are nonzero values—this is a prerequisite for any triangle. Following this, introduced values should be organized in a specific order (usually ascending) so the algorithm can correctly identify the longest side presumed to be the hypotenuse.

After the values are sorted, the program calculates the squares of these values. Finally, the logic compares the calculated squares of the shorter sides with the square of the presumed hypotenuse to confirm or deny the existence of a right triangle based on the Pythagorean principle.

Conditional Statements in Java

In Java, conditional statements control the flow of execution based on the truthfulness of specified conditions. They are used to perform different actions for different decisions. The most common conditional statements are \( if \) statements, \( else \) clauses, and \( else if \) combinations, which help in making decisions.

When implementing the Pythagorean theorem in Java, you would employ an \( if \) statement to check if the sum of the squares of the two smaller numbers indeed equals the square of the largest number. The syntax for such a conditional statement would be:
\( if(a^2 + b^2 == c^2) \), where \( a \) and \( b \) are the shorter sides, and \( c \) is the hypotenuse.

An \( if \) statement is accompanied by a block of code that gets executed only when the condition evaluates to true. If the triangle sides do not meet the Pythagorean condition, an \( else \) clause can be used to execute an alternative block of code. This effective use of conditional statements ensures the Java program can correctly identify right triangles and communicate the results to the user.