Question
What is the length of the hypotenuse? The legs are 48 ft and 55 ft. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the hypotenuse in a right triangle given the lengths of the legs, you can use the Pythagorean theorem, which states that:
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, the legs are 48 ft and 55 ft.
1. First, calculate \(a^2\) and \(b^2\):
\[
48^2 = 2304
\]
\[
55^2 = 3025
\]
2. Now add these two values together:
\[
c^2 = 2304 + 3025 = 5329
\]
3. To find \(c\), take the square root of \(5329\):
\[
c = \sqrt{5329} = 73
\]
Thus, the length of the hypotenuse is \(73\) ft.
Final answer: **73 ft**.
\[
c^2 = a^2 + b^2
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the legs. In this case, the legs are 48 ft and 55 ft.
1. First, calculate \(a^2\) and \(b^2\):
\[
48^2 = 2304
\]
\[
55^2 = 3025
\]
2. Now add these two values together:
\[
c^2 = 2304 + 3025 = 5329
\]
3. To find \(c\), take the square root of \(5329\):
\[
c = \sqrt{5329} = 73
\]
Thus, the length of the hypotenuse is \(73\) ft.
Final answer: **73 ft**.