The hypotenuse of a right triangle can be found using the Pythagorean theorem: a² + b² = c², where 'c' is the hypotenuse, and 'a' and 'b' are the lengths of the other two sides (legs) of the triangle.
Steps to Find the Hypotenuse:
- Identify the Right Triangle: Make sure you're working with a right triangle, which has one angle that measures 90 degrees. The hypotenuse is always opposite the right angle.
- Identify the Legs: The two sides that form the right angle are called legs, and are represented by 'a' and 'b' in the Pythagorean theorem. It doesn't matter which leg you call 'a' and which you call 'b'.
- Apply the Pythagorean Theorem: The theorem states a² + b² = c², where 'c' is the length of the hypotenuse.
- Substitute the Values: Plug in the known values of 'a' and 'b' into the equation.
- Calculate the Squares: Calculate a² and b².
- Add the Squares: Add the results of a² + b².
- Find the Square Root: Take the square root of the sum you calculated in the previous step. This will give you the length of the hypotenuse, 'c'.
Example:
Let's say you have a right triangle with legs of length 3 and 4.
- a = 3, b = 4
- a² = 3² = 9
- b² = 4² = 16
- a² + b² = 9 + 16 = 25
- c² = 25
- c = √25 = 5
Therefore, the hypotenuse of the triangle is 5.
In summary, the Pythagorean theorem (a² + b² = c²) is your key to finding the hypotenuse, provided you know the lengths of the other two sides of the right triangle.
