Question

If a right triangle has a leg with length 12 in. and the hypotenuse is 16 in., the other leg must be approximately [blank] in

11.5
10.6
20
8.6

Answer 1

To find the length of the other leg in a right triangle, we can use the Pythagorean theorem, which states:

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

Where:
- \( a \) and \( b \) are the lengths of the legs,
- \( c \) is the length of the hypotenuse.

In this case, one leg \( a = 12 \) in and the hypotenuse \( c = 16 \) in. We need to find the length of the other leg \( b \).

Substituting the known values into the theorem gives us:

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

Calculating the squares:

\[
144 + b^2 = 256
\]

Now, subtract 144 from both sides:

\[
b^2 = 256 - 144
\]
\[
b^2 = 112
\]

Next, take the square root of both sides to find \( b \):

\[
b = \sqrt{112}
\]
\[
b \approx 10.583
\]

Thus, the length of the other leg is approximately \( 10.6 \) in.

So, the answer is **10.6** in.