Question

What is the length of the hypotenuse? The legs are 84 ft and 35 ft. If necessary, round to the nearest tenth.

Answer 1

To find the length of the hypotenuse of a right triangle when the lengths of the legs are known, you can use the Pythagorean theorem. The theorem states:

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

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

In this case, the lengths of the legs are:

- \(a = 84\) ft
- \(b = 35\) ft

Now, substitute the values into the formula:

\[
c = \sqrt{(84)^2 + (35)^2}
\]

First, calculate \(84^2\) and \(35^2\):

\[
84^2 = 7056
\]
\[
35^2 = 1225
\]

Now, add these two values together:

\[
c = \sqrt{7056 + 1225}
\]
\[
c = \sqrt{8271}
\]

Now calculate \(\sqrt{8271}\):

\[
c \approx 90.9
\]

Thus, the length of the hypotenuse, rounded to the nearest tenth, is approximately **90.9 ft**.