Find BC in Right Triangle ABC: Given AB = 6 and Hypotenuse AC = 20

To solve for $BC$ in the right triangle $\triangle ABC$, we follow these steps:

• Identify the given lengths: $AB = 6$ and $AC = 20$.
• Apply the Pythagorean Theorem: $AB^2 + BC^2 = AC^2$.
• Substitute known values into the formula:

$6^2 + BC^2 = 20^2$

Simplify the left side:

$36 + BC^2 = 400$

Subtract 36 from both sides:

$BC^2 = 400 - 36$

$BC^2 = 364$

Solve for $BC$ by taking the square root of both sides:

$BC = \sqrt{364}$

Thus, the length of $BC$ is $\sqrt{364}$.