The hypotenuse of a right triangle measures 4 cm and one of its legs measures 1 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 a right triangle when one leg and the hypotenuse are known, 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 of the triangle.

In this case, we know:

  • The hypotenuse \(c = 4\) cm
  • One leg \(a = 1\) cm

We need to find the length of the other leg \(b\).

Substituting the values into the Pythagorean theorem:

\[ 1^2 + b^2 = 4^2 \]

This simplifies to:

\[ 1 + b^2 = 16 \]

Now, subtract 1 from both sides:

\[ b^2 = 16 - 1 \]

\[ b^2 = 15 \]

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

\[ b = \sqrt{15} \]

Calculating \(\sqrt{15}\):

\[ b \approx 3.87298 \]

Rounding to the nearest tenth:

\[ b \approx 3.9 \]

Therefore, the length of the other leg is approximately 3.9 cm.