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 of the right triangle, we can use the Pythagorean theorem, which states:

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

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 \( a = 12 \)
- The hypotenuse \( c = 16 \)
- We need to find the length of the other leg \( b \).

Plugging the known values into the equation gives us:

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

Calculating the squares:

\[
144 + b^2 = 256
\]

Next, we isolate \( b^2 \) by subtracting 144 from both sides:

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

Now, we take the square root of both sides to solve for \( b \):

\[
b = \sqrt{112}
\]

Calculating the square root:

\[
b \approx 10.583
\]

Rounding to the nearest tenth gives:

\[
b \approx 10.6
\]

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