Question

One of the legs of a right triangle measures 13 cm and its hypotenuse measures 17 cm. Find the measure of the other leg. If necessary, round to the nearest tenth.

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

In this case, we know one leg \(a = 13\) cm and the hypotenuse \(c = 17\) cm. We need to find the other leg \(b\). We can rearrange the Pythagorean theorem to solve for \(b\):

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

Substituting the known values into the equation:

\[
b^2 = 17^2 - 13^2
\]

Calculating \(17^2\) and \(13^2\):

\[
17^2 = 289
\]

\[
13^2 = 169
\]

Now substituting these values back into the equation:

\[
b^2 = 289 - 169
\]

\[
b^2 = 120
\]

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

\[
b = \sqrt{120}
\]

Calculating the square root:

\[
b \approx 10.95
\]

Rounding to the nearest tenth gives:

\[
b \approx 11.0 \text{ cm}
\]

Thus, the measure of the other leg is approximately **11.0 cm**.