Question

One of the legs of a right triangle measures 4 cm and its hypotenuse measures 16 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 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**.