Question

(1 point)
If a right triangle has a leg with length 12 in. and the hypotenuse is 16 in., the other leg must be approximately
in..

Answer 1

To find the length of the other leg of a right triangle when one leg and the hypotenuse are known, we can use the Pythagorean theorem:

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

where \(c\) is the hypotenuse, and \(a\) and \(b\) are the legs of the triangle.

In this case:
- One leg (\(a\)) is 12 in.
- The hypotenuse (\(c\)) is 16 in.

Let's denote the other leg as \(b\). We can rearrange the Pythagorean theorem to solve for \(b\):

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

Substituting the known values:

\[
b^2 = 16^2 - 12^2
\]

Calculating the squares:

\[
b^2 = 256 - 144
\]

\[
b^2 = 112
\]

Now, taking the square root to find \(b\):

\[
b = \sqrt{112}
\]

Calculating this gives:

\[
b \approx 10.583
\]

Thus, the length of the other leg is approximately **10.58 in.**