Find AB in Right Triangle ABC: Given BC = 6 and Hypotenuse with √2

To find the length of side AB in the right triangle ABC:

• Step 1: Identify the known lengths. We know $BC = 6$ and $AC = \sqrt{72}$.
• Step 2: Apply the Pythagorean Theorem: $AB^2 + BC^2 = AC^2$.
• Step 3: Plug in the known values: $AB^2 + 6^2 = (\sqrt{72})^2$.
• Step 4: Since $(\sqrt{72})^2 = 72$, the equation becomes $AB^2 + 36 = 72$.
• Step 5: Subtract 36 from both sides, yielding: $AB^2 = 36$.
• Step 6: Take the square root of each side: $AB = \sqrt{36} = 6$.

Thus, the length of side AB is $6$.