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.

1 answer

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.