Find Side AB in Right Triangle ABC: Given Hypotenuse 10 and Base 5

To find the length of side $AB$ in the right triangle $ABC$, we will use the Pythagorean theorem:

Since $BC$ is the hypotenuse, $BC = 10$, and one leg $AC = 5$, we can express the Pythagorean theorem as:

$AB^2 + AC^2 = BC^2$

Substituting the known values gives us:

$AB^2 + 5^2 = 10^2$

Simplifying further:

$AB^2 + 25 = 100$

Subtracting 25 from both sides results in:

$AB^2 = 75$

Taking the square root of both sides, we obtain:

$AB = \sqrt{75}$

Therefore, the length of side $AB$ is $\sqrt{75}$.