Question
What is the length of the missing leg? One of the legs are 60 m and the slope is 100 m If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg of a right triangle, you can use the Pythagorean theorem, which states that:
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) and \(b\) are the lengths of the legs,
- \(c\) is the length of the hypotenuse (the slope in this case).
In your problem:
- One leg (\(a\)) is 60 m,
- The hypotenuse (\(c\)) is 100 m.
We need to find the other leg (\(b\)). Rearranging the Pythagorean theorem gives:
\[
b^2 = c^2 - a^2
\]
Now substituting the known values:
\[
b^2 = 100^2 - 60^2
\]
Calculating the squares:
\[
b^2 = 10000 - 3600
\]
\[
b^2 = 6400
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{6400} = 80
\]
Thus, the length of the missing leg is **80 m**.
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) and \(b\) are the lengths of the legs,
- \(c\) is the length of the hypotenuse (the slope in this case).
In your problem:
- One leg (\(a\)) is 60 m,
- The hypotenuse (\(c\)) is 100 m.
We need to find the other leg (\(b\)). Rearranging the Pythagorean theorem gives:
\[
b^2 = c^2 - a^2
\]
Now substituting the known values:
\[
b^2 = 100^2 - 60^2
\]
Calculating the squares:
\[
b^2 = 10000 - 3600
\]
\[
b^2 = 6400
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{6400} = 80
\]
Thus, the length of the missing leg is **80 m**.