The Pythagorean theorem is a fundamental principle in geometry that relates the lengths of the sides of a right triangle. Here's how to understand and use it:
What is the Pythagorean Theorem?
For a right triangle (a triangle with one 90-degree angle), the theorem states:
a2+b2=c2a^2+b^2=c^2a2+b2=c2
- a and b are the lengths of the two legs (the sides that form the right angle).
- c is the length of the hypotenuse (the side opposite the right angle, and the longest side).
How to Use the Pythagorean Theorem
Step 1: Identify the sides
- Find the two legs (a and b).
- Identify the hypotenuse (c).
Step 2: Plug the known values into the formula
- If you know the lengths of the legs and want to find the hypotenuse:
c=a2+b2c=\sqrt{a^2+b^2}c=a2+b2
- If you know the hypotenuse and one leg, and want to find the other leg:
a=c2−b2orb=c2−a2a=\sqrt{c^2-b^2}\quad \text{or}\quad b=\sqrt{c^2-a^2}a=c2−b2orb=c2−a2
Step 3: Calculate
- Square the known side lengths.
- Add or subtract as needed.
- Take the square root to find the missing side.
Example
Suppose you have a right triangle with legs of length 3 and 4, and you want to find the hypotenuse.
c=32+42=9+16=25=5c=\sqrt{3^2+4^2}=\sqrt{9+16}=\sqrt{25}=5c=32+42=9+16=25=5
So, the hypotenuse is 5. If you want, I can help you solve a specific problem using the Pythagorean theorem!
