Question

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

Answer 1

I'll round it up to 10.6

Answer 2

To find the length of the other leg in a right triangle where one leg is 12 inches and the hypotenuse is 16 inches, we can use the Pythagorean theorem:

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

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

- One leg \( a = 12 \) inches
- Hypotenuse \( c = 16 \) inches

We need to find the other leg \( b \). Plugging in the values we have:

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

Calculating the squares:

\[
144 + b^2 = 256
\]

Subtracting 144 from both sides:

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

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

\[
b = \sqrt{112}
\]

We can simplify \( \sqrt{112} \):

\[
\sqrt{112} = \sqrt{16 \times 7} = \sqrt{16} \times \sqrt{7} = 4\sqrt{7}
\]

Using a calculator for an approximate value of \( \sqrt{7} \approx 2.64575 \):

\[
b \approx 4 \times 2.64575 \approx 10.583
\]

Thus, the length of the other leg is approximately \( 10.58 \) inches.

Therefore, the other leg must be approximately **10.58 inches**.