# 1. Introduction

The Pythagorean Theorem is a fundamental principle in trigonometry that establishes a relationship between the lengths of the sides of a right triangle.

Specifically, the theorem states that 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. Mathematically, this is represented as c^2 = a^2 + b^2, where c is the hypotenuse and a and b are the other two sides.

This guide demonstrates a Ruby program to calculate the length of the hypotenuse given the lengths of the other two sides.

# 2. Program Steps

1. Prepare your Ruby development environment.

2. Prompt the user to input the lengths of the two sides of the right triangle.

3. Use the Pythagorean theorem formula to compute the length of the hypotenuse.

4. Display the computed hypotenuse length to the user.

# 3. Code Program

``````# Prompting the user for the lengths of the two sides
puts "Enter the length of side a:"
a = gets.chomp.to_f
puts "Enter the length of side b:"
b = gets.chomp.to_f
# Calculate the length of the hypotenuse using the Pythagorean theorem
hypotenuse = Math.sqrt(a**2 + b**2)
# Display the result
puts "The length of the hypotenuse is: #{hypotenuse.round(2)}"
``````

### Output:

```Enter the length of side a:
3
Enter the length of side b:
4
The length of the hypotenuse is: 5.0
```

### Explanation:

1. gets: This method is used to capture user input. The input is taken as a string by default.

2. chomp: A string method that removes the newline character appended when the user presses Enter.

3. to_f: Converts the input string to a floating-point number. This allows for more precise calculations, especially when dealing with non-integer side lengths.

4. Math.sqrt: Ruby's built-in method to compute the square root of a number.

5. a2 and b2: In Ruby, the operator is used for exponentiation. These expressions square the lengths of the respective sides.