Overview
This lecture explains how to find the length of the hypotenuse of a right triangle using the Pythagorean theorem, with step-by-step examples.
Pythagorean Theorem Basics
- The Pythagorean theorem states: a² + b² = c².
- In this formula, a and b are the legs (shorter sides), and c is always the hypotenuse (longest side).
- The hypotenuse is the side opposite the right angle in a right triangle.
- You can use this theorem if you know the lengths of any two sides of a right triangle.
Example 1: Solving for Hypotenuse (Whole Number)
- Given: a = 8 meters, b = 6 meters.
- Plug values into the formula: 8² + 6² = c².
- Calculate: 64 + 36 = 100; so 100 = c².
- Take the square root of both sides: c = √100 = 10.
- The hypotenuse measures 10 meters.
Example 2: Solving for Hypotenuse (Decimal Answer)
- Given: a = 10 feet, b = 7 feet.
- Plug values into the formula: 10² + 7² = c².
- Calculate: 100 + 49 = 149; so 149 = c².
- Take the square root of both sides: c = √149.
- Since 149 is not a perfect square, √149 ≈ 12.206 (rounded to 12.21).
- The hypotenuse is approximately 12.21 feet.
Key Terms & Definitions
- Pythagorean theorem — A formula to relate the side lengths of a right triangle: a² + b² = c².
- Hypotenuse — The longest side of a right triangle, opposite the right angle.
- Legs (of a triangle) — The two sides that form the right angle.
- Perfect square — A number that has an integer as its square root.
- Irrational number — A decimal that neither terminates nor repeats (like √149).
Action Items / Next Steps
- Practice solving for the hypotenuse with different right triangle side lengths.
- Review how to round square roots to the nearest hundredth.
- Complete any assigned homework problems using the Pythagorean theorem.