Find the Hypotenuse AC in a Right Triangle with Legs 7 and 1

To find the length of AC, the hypotenuse of the right triangle ABC, we will apply the Pythagorean Theorem:

The Pythagorean Theorem states:

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

where $a$ and $b$ are the legs ($AB$ and $BC$), and $c$ is the hypotenuse ($AC$).
Given: $AB = 7$ and $BC = 1$.

Substituting the given values into the theorem:

$(7)^2 + (1)^2 = AC^2$.

Calculating the squares:

$49 + 1 = AC^2$.

Simplifying the equation:

$50 = AC^2$.

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

$AC = \sqrt{50}$.

Therefore, the length of AC is $\sqrt{50}$.