Question

A student is asked to find the length of the hypotenuse of a right triangle. The length of one leg is 32 ​centimeters, and the length of the other leg is 23 centimeters. The student incorrectly says that the length of the hypotenuse is 7.4 centimeters. Answer parts a and b.
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Part 1
a. Find the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter.
The length of the hypotenuse of the right triangle to the nearest tenth of a centimeter is
  
enter your response here cm.
​(Round to the nearest tenth as​ needed.)

Answer 1

To find the length of the hypotenuse of a right triangle given the lengths of the two legs, we can use the Pythagorean theorem:

\[
c = \sqrt{a^2 + b^2}
\]

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

Given:
- \(a = 32\) cm (one leg)
- \(b = 23\) cm (the other leg)

Now we can substitute the values into the formula:

\[
c = \sqrt{32^2 + 23^2}
\]

Calculating \(32^2\) and \(23^2\):

\[
32^2 = 1024
\]
\[
23^2 = 529
\]

Now we add these together:

\[
c = \sqrt{1024 + 529} = \sqrt{1553}
\]

Next, we find the square root of 1553:

\[
c \approx 39.4 \, \text{cm} \, (to \, the \, nearest \, tenth)
\]

So, the length of the hypotenuse of the right triangle to the nearest tenth of a centimeter is:

**39.4 cm**.

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