Exercise 4 - Pythagorean Theorem

Exercise 4

The Pythagorean theorem states that for a right triangle, the relationship between the length of the hypotenuse \( c \) and the lengths of the other sides \( a \) and \( b \) is given by:

\[c^2 = a^2 + b^2\]

Write a script that will prompt the user for the lengths \( a \) and \( c \), call a function findb to calculate and return the length of \( b \), and print the result. Note that any values of \( a \) or \( c \) that are less than or equal to zero would not make sense, so the script should print an error message if the user enters any invalid value.

Right Triangle Diagram:
Hypotenuse (c) is the longest side, opposite the right angle
Sides a and b form the right angle

Provided Function: findb.m

                    function b = findb(a,c)

                    % Calculates b from a and c

                    b = sqrt(c^2 - a^2);

                    end

Script Requirements:

Prompt user for input values of a and c
Validate that both inputs are positive numbers
Call the findb function to calculate b
Display the calculated value of b
Include error handling for invalid inputs

Input Validation Rules:

a > 0 (must be positive)
c > 0 (must be positive)
c > a (hypotenuse must be longer than side a)
c² ≥ a² (to avoid imaginary numbers)

Expected Program Flow:

Prompt for side a
If a ≤ 0, display error and exit
Prompt for hypotenuse c
If c ≤ 0, display error and exit
If c ≤ a, display error and exit
Calculate b = findb(a, c)
Display result: "The length of side b is X"

Mathematical Rearrangement:

From the Pythagorean theorem: c² = a² + b²

Solving for b: b² = c² - a²

Therefore: b = √(c² - a²)