To find the length of the other leg of a right triangle, 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 two legs.
In this problem, we know:
- One leg \( a = 4 \) cm (we will use this as one of the legs),
- Hypotenuse \( c = 16 \) cm,
- We need to find the other leg \( b \).
Plugging the known values into the Pythagorean theorem gives us:
\[ 4^2 + b^2 = 16^2 \]
Calculating the squares, we get:
\[ 16 + b^2 = 256 \]
Next, we isolate \( b^2 \) by subtracting 16 from both sides:
\[ b^2 = 256 - 16 \]
\[ b^2 = 240 \]
Now, we take the square root of both sides to find \( b \):
\[ b = \sqrt{240} \]
To simplify \( \sqrt{240} \), we can factor it:
\[ \sqrt{240} = \sqrt{16 \times 15} = \sqrt{16} \times \sqrt{15} = 4\sqrt{15} \]
Now let's calculate \( 4\sqrt{15} \) to get a numerical approximation. We know that \(\sqrt{15} \approx 3.872\), thus:
\[ 4\sqrt{15} \approx 4 \times 3.872 \approx 15.488 \]
Rounding to the nearest tenth, we find:
\[ b \approx 15.5 \text{ cm} \]
Thus, the length of the other leg is approximately 15.5 cm.