Question
if it is a right traingle and one side is 14 miles and the bottom is 7 miles what is the last side?
Answers
GPT-4o mini
To calculate the length of the last side of a right triangle where you have one side of 14 miles (let's assume it's the vertical leg) and the other side (the horizontal leg) is 7 miles, you can use the Pythagorean theorem:
\[
c^2 = a^2 + b^2
\]
where:
- \(c\) is the length of the hypotenuse,
- \(a\) and \(b\) are the lengths of the other two sides.
Here, let’s assign:
- \(a = 7\) miles (one leg),
- \(b = 14\) miles (the other leg).
Plugging the values into the equation gives:
\[
c^2 = 7^2 + 14^2
\]
\[
c^2 = 49 + 196
\]
\[
c^2 = 245
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{245} \approx 15.65 \text{ miles}
\]
So the length of the hypotenuse (the last side) is approximately 15.65 miles.
\[
c^2 = a^2 + b^2
\]
where:
- \(c\) is the length of the hypotenuse,
- \(a\) and \(b\) are the lengths of the other two sides.
Here, let’s assign:
- \(a = 7\) miles (one leg),
- \(b = 14\) miles (the other leg).
Plugging the values into the equation gives:
\[
c^2 = 7^2 + 14^2
\]
\[
c^2 = 49 + 196
\]
\[
c^2 = 245
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{245} \approx 15.65 \text{ miles}
\]
So the length of the hypotenuse (the last side) is approximately 15.65 miles.