Question

57 ft length and 76 ft height
What is the length of the hypotenuse? If necessary, round to the nearest tenth.
c =__ feet

Answer 1

To find the length of the hypotenuse \( c \) in a right triangle where the lengths of the two legs are given, you can use the Pythagorean theorem:

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

In this case, the lengths of the legs are:
- \( a = 57 \) ft (length)
- \( b = 76 \) ft (height)

Now plug in the values:

\[
c = \sqrt{(57)^2 + (76)^2}
\]

Calculating the squares:

\[
57^2 = 3249
\]
\[
76^2 = 5776
\]

Adding these together:

\[
c = \sqrt{3249 + 5776} = \sqrt{9025}
\]

Finding the square root:

\[
c = 95
\]

Therefore, the length of the hypotenuse is:

\[
c = 95 \text{ feet}
\]