Question

If a right triangle has a leg with length 12 and the hypotenuse is 16, how long is the other leg? Round to the nearest tenth, if necessary.(1 point).

Answer 1

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

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

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

In this case, let \( a = 12 \), \( c = 16 \), and \( b \) be the unknown leg. We can rearrange the formula to solve for \( b \):

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

Now, plugging in the values:

\[ b^2 = 16^2 - 12^2 \]
\[ b^2 = 256 - 144 \]
\[ b^2 = 112 \]

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

\[ b = \sqrt{112} \]

To simplify \( \sqrt{112} \):

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

Now, calculating \( 4\sqrt{7} \):

Using a calculator, \( \sqrt{7} \approx 2.6458 \).

Thus,

\[ b \approx 4 \times 2.6458 \approx 10.5832 \]

Rounding to the nearest tenth:

\[ b \approx 10.6 \]

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