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.