How do u find the length of an unknown leg in a right triangle

To find the length of an unknown leg in a right triangle, you can use the Pythagorean theorem, which states:

\[
a^2 + b^2 = c^2
\]

Here, \(a\) and \(b\) represent the lengths of the two legs of the triangle, and \(c\) represents the length of the hypotenuse (the side opposite the right angle).

If you know the length of one leg and the hypotenuse, you can rearrange the equation to find the unknown leg. For example:

1. If you know leg \(a\) and the hypotenuse \(c\), to find leg \(b\), use:
\[
b = \sqrt{c^2 - a^2}
\]

2. If you know leg \(b\) and the hypotenuse \(c\), to find leg \(a\), use:
\[
a = \sqrt{c^2 - b^2}
\]

### Example:
If a right triangle has a hypotenuse of length 10 units and one leg measuring 6 units, you can find the other leg as follows:

1. Identify the known values:
- \(c = 10\)
- \(a = 6\) (we need to find \(b\))

2. Use the formula:
\[
b = \sqrt{c^2 - a^2} = \sqrt{10^2 - 6^2} = \sqrt{100 - 36} = \sqrt{64} = 8
\]

So, the unknown leg \(b\) is 8 units long.