How to Solve for B Using the Pythagorean Theorem with Sides 6mm and 5mm

The Pythagorean theorem is a fundamental rule in geometry that states for a right triangle, the square of the hypotenuse (c) is equal to the sum of the squares of the other two sides (a and b):

c² = a² + b²

If you are given two sides (6mm and 5mm) and you want to find the third side B, here is how to proceed step by step depending on which side you want to find:

1. Identify the sides: Let's say the sides are: 6mm and 5mm, and you want to find side B.
2. Determine if B is the hypotenuse or a leg:
   • If B is the hypotenuse (the longest side opposite the right angle), then B² = 6² + 5²
   • If B is one of the legs, and let's say the hypotenuse is 6mm, then B² = 6² - 5²
3. Calculate accordingly:
   • Case 1: B is the hypotenuse:

   B² = 6² + 5² = 36 + 25 = 61

   B = √61 ≈ 7.81mm

   • Case 2: B is a leg and hypotenuse is 6mm:

   B² = 6² - 5² = 36 - 25 = 11

   B = √11 ≈ 3.32mm

Summary: To find B using the Pythagorean theorem, first identify whether B is the hypotenuse or a leg, then apply the formula accordingly, and finally calculate the square root to get B.