Questions: The Pythagorean Theorem is c^2=a^2-b^2

Transcript text: The Pythagorean Theorem is \[ c^{2}=a^{2}-b^{2} \]

Solution

Step 1: Identify the Sides

Given the lengths of the two sides of a right triangle, \( a = 3 \) and \( b = 4 \), we need to find the length of the hypotenuse \( c \).

Step 2: Apply the Pythagorean Theorem

Using the Pythagorean Theorem, we have: \[ c^2 = a^2 + b^2 \] Substituting the values of \( a \) and \( b \): \[ c^2 = 3^2 + 4^2 = 9 + 16 = 25 \]

Step 3: Calculate the Hypotenuse

Taking the square root of both sides to find \( c \): \[ c = \sqrt{25} = 5.0 \]

\(\boxed{c = 5}\)

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