Question
What is the length of the missing leg? One leg is 9.4 km and the slope is 9.7 km If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the missing leg in a right triangle, you can use the Pythagorean theorem, which states:
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) and \(b\) are the lengths of the legs, and
- \(c\) is the length of the hypotenuse (the slope in this case).
Given:
- One leg \(a = 9.4\) km
- The hypotenuse \(c = 9.7\) km
We need to find the other leg \(b\).
Rearranging the Pythagorean theorem gives us:
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = (9.7)^2 - (9.4)^2
\]
Calculating the squares:
\[
b^2 = 94.09 - 88.36
\]
\[
b^2 = 5.73
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{5.73} \approx 2.4
\]
So, the length of the missing leg is approximately **2.4 km**.
\[
a^2 + b^2 = c^2
\]
where:
- \(a\) and \(b\) are the lengths of the legs, and
- \(c\) is the length of the hypotenuse (the slope in this case).
Given:
- One leg \(a = 9.4\) km
- The hypotenuse \(c = 9.7\) km
We need to find the other leg \(b\).
Rearranging the Pythagorean theorem gives us:
\[
b^2 = c^2 - a^2
\]
Substituting the known values:
\[
b^2 = (9.7)^2 - (9.4)^2
\]
Calculating the squares:
\[
b^2 = 94.09 - 88.36
\]
\[
b^2 = 5.73
\]
Now, take the square root of both sides to find \(b\):
\[
b = \sqrt{5.73} \approx 2.4
\]
So, the length of the missing leg is approximately **2.4 km**.