Question
What is the length of the hypotenuse? The legs are 8 yd and 6 yd. If necessary, round to the nearest tenth.
Answers
GPT-4o mini
To find the length of the hypotenuse in a right triangle with legs of lengths 8 yards and 6 yards, you can use the Pythagorean theorem, which states:
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
In this case, \(a = 8\) yards and \(b = 6\) yards. Plugging in these values, you get:
\[
c = \sqrt{8^2 + 6^2}
\]
Calculating \(8^2\) and \(6^2\):
\[
c = \sqrt{64 + 36}
\]
\[
c = \sqrt{100}
\]
Now, take the square root of 100:
\[
c = 10
\]
Thus, the length of the hypotenuse is **10 yards**.
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two legs.
In this case, \(a = 8\) yards and \(b = 6\) yards. Plugging in these values, you get:
\[
c = \sqrt{8^2 + 6^2}
\]
Calculating \(8^2\) and \(6^2\):
\[
c = \sqrt{64 + 36}
\]
\[
c = \sqrt{100}
\]
Now, take the square root of 100:
\[
c = 10
\]
Thus, the length of the hypotenuse is **10 yards**.