Question

If a right triangle has a leg with a length of 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 of the right triangle, we can use the Pythagorean theorem, which states that in a right triangle:

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

where \( c \) is the length of the hypotenuse, and \( a \) and \( b \) are the lengths of the legs. In this case, we know one leg \( a = 12 \) and the hypotenuse \( c = 16 \).

Substituting the known values into the equation:

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

Calculating the squares:

\[ 144 + b^2 = 256 \]

Next, subtract 144 from both sides:

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

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

\[ b = \sqrt{112} \]

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

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

Calculating \( \sqrt{7} \) (approximately 2.64575):

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

Rounding to the nearest tenth:

\[ b \approx 10.6 \]

Thus, the length of the other leg is approximately **10.6**.