Question

Triangles Unit Test
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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 when one leg (a) and the hypotenuse (c) are known, we can use the Pythagorean theorem, which states:

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

Here, \(a\) is one leg (12 in this case), \(b\) is the other leg, and \(c\) is the hypotenuse (16).

Plugging in the values:

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

Calculating \(12^2\) and \(16^2\):

\[ 144 + b^2 = 256 \]

Now, subtract 144 from both sides:

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

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

\[ b = \sqrt{112} \]

Simplifying this:

\[ b \approx 10.583 \]

Rounding to the nearest tenth:

\[ b \approx 10.6 \]

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