Find BC in Right Triangle ABC: Given Leg AB = 3 and Hypotenuse AC = 5

To solve this problem, we'll perform the following steps:

• Step 1: Identify the sides of the triangle. The problem states $AB = 5$ and $AC = 3$. Since triangle ABC is a right triangle, $AB = 5$ is the hypotenuse.

• Step 2: Apply the Pythagorean Theorem, which states $a^2 + b^2 = c^2$, where $c$ is the hypotenuse.

• Step 3: In this case, set $CA = 3$, $BC = x$, and $AB = 5$. Substitute these into the theorem:
  $3^2 + x^2 = 5^2$

• Step 4: Calculate $3^2 = 9$ and $5^2 = 25$. Thus, the equation becomes:
  $9 + x^2 = 25$

• Step 5: Rearrange to solve for $x^2$:
  $x^2 = 25 - 9$
  $x^2 = 16$

• Step 6: Solve for $x$ by taking the square root:
  $x = \sqrt{16} = 4$

Therefore, the length of side BC is $4$.