To use the Pythagorean theorem, follow these steps:

1. Identify the right triangle and its sides :
   • Confirm the triangle has a right angle (90 degrees).
   • Label the two shorter sides (legs) as aaa and bbb.
   • Label the longest side opposite the right angle as ccc, called the hypotenuse

2. Use the Pythagorean theorem formula :

a2+b2=c2a^2+b^2=c^2a2+b2=c2

This means the sum of the squares of the legs equals the square of the hypotenuse

3. Solve for the missing side :
   • If you need to find the hypotenuse ccc, rearrange the formula:

c=a2+b2c=\sqrt{a^2+b^2}c=a2+b2​

 * If you need to find a leg aaa or bbb, rearrange the formula:

a=c2−b2orb=c2−a2a=\sqrt{c^2-b^2}\quad \text{or}\quad b=\sqrt{c^2-a^2}a=c2−b2​orb=c2−a2​

Substitute the known side lengths and calculate the square root to find the missing length

Example :
If one leg is 5 units and the other leg is 12 units, to find the hypotenuse ccc:

c2=52+122=25+144=169c^2=5^2+12^2=25+144=169c2=52+122=25+144=169

c=169=13c=\sqrt{169}=13c=169​=13

So, the hypotenuse is 13 units long

. This method works for any right triangle to find the length of any side when the other two are known