Find the Hypotenuse AC in Right Triangle ABC with Legs 6 and 5

To solve this problem, we will use the Pythagorean Theorem. It states that for a right triangle with sides $a$ and $b$, and hypotenuse $c$, the relationship is given by:

$a^2 + b^2 = c^2$

In triangle ABC, let $AB = a = 6$ and $BC = b = 5$. We need to find the length of the hypotenuse $AC = c$.

Applying the Pythagorean Theorem, we have:

$6^2 + 5^2 = c^2$

$36 + 25 = c^2$

$61 = c^2$

To find $c$, we take the square root of both sides:

$c = \sqrt{61}$

Thus, the length of AC is $\sqrt{61}$.