Question

One of the legs of a right triangle measures 16 cm and its hypotenuse measures 20 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

Answer 1

To find the measure of the other leg in a right triangle, we can use the Pythagorean theorem, which states:

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

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

In this case, we know:
- One leg \(a = 16 \, \text{cm}\)
- The hypotenuse \(c = 20 \, \text{cm}\)

We need to find the other leg \(b\). Plugging the known values into the Pythagorean theorem gives us:

\[
16^2 + b^2 = 20^2
\]

Calculating the squares:

\[
256 + b^2 = 400
\]

Now, subtract \(256\) from both sides to isolate \(b^2\):

\[
b^2 = 400 - 256
\]
\[
b^2 = 144
\]

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

\[
b = \sqrt{144} = 12 \, \text{cm}
\]

Thus, the measure of the other leg is:

\[
\boxed{12} \, \text{cm}
\]