Pythagorean Theorem (a² + b² = c²) Practice Problems & Right Triangle Solutions
Master the Pythagorean Theorem for right triangles: solve for the hypotenuse c = √(a² + b²), recover missing legs a = √(c² − b²), and memorize essential Pythagorean integer triples.
🧠 Core Problem-Solving Strategies
📐 Hypotenuse Formula: c = √(a² + b²)
Square both legs, add the results, and take the square root: For legs 6 and 8: c = √(36 + 64) = √100 = 10.
🔍 Missing Leg Formula: a = √(c² − b²)
Subtract the square of the known leg from the square of the hypotenuse: For c=13, b=12: a = √(169 − 144) = √25 = 5.
⚡ Pythagorean Integer Triples Memorization
Recognize fundamental triples: (3, 4, 5), (5, 12, 13), (8, 15, 17), (7, 24, 25), and their scalar multiples (e.g. 6, 8, 10).
❓ Frequently Asked Questions
What is the Pythagorean Theorem formula?
The formula is a² + b² = c², where a and b are the lengths of the legs meeting at the 90-degree right angle, and c is the longest opposite side (hypotenuse).
Can the Pythagorean Theorem be used on any triangle?
NO. It applies ONLY to right triangles (triangles with exactly one 90-degree angle).
Continue Learning & Practicing
Reinforce your understanding with printable worksheets, step-by-step guides, calculators, and speed games: