Question

One of the legs of a right triangle measures 16 cm and the other leg measures 10 cm. Find the measure of the hypotenuse. If necessary, round to the nearest tenth.

Answer 1

To find the hypotenuse of a right triangle when the lengths of the two legs are given, we can use the Pythagorean theorem, which states:

\[
c^2 = a^2 + b^2
\]

where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs.

In this case, we have:

- \(a = 16 \, \text{cm}\)
- \(b = 10 \, \text{cm}\)

Now we can substitute the values into the formula:

\[
c^2 = 16^2 + 10^2
\]

Calculating the squares:

\[
c^2 = 256 + 100
\]

Now, adding these values together:

\[
c^2 = 356
\]

Next, we take the square root of both sides to find \(c\):

\[
c = \sqrt{356}
\]

Calculating the square root:

\[
c \approx 18.9 \, \text{cm} \quad (\text{rounded to the nearest tenth})
\]

Thus, the measure of the hypotenuse is approximately \( \boxed{18.9} \, \text{cm} \).