Question
what is the length of the hypotenuse if necessary round to the nearest tenth 9 yd and 3 yd
Answers
GPT-4o mini
To find the length of the hypotenuse of a right triangle when you know the lengths of the other two sides (the legs), you can use the Pythagorean theorem:
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In your case, \(a = 9\) yards and \(b = 3\) yards.
Now, plug in the values:
\[
c = \sqrt{9^2 + 3^2}
\]
Calculating the squares:
\[
c = \sqrt{81 + 9}
\]
\[
c = \sqrt{90}
\]
Now, calculate \(\sqrt{90}\):
\[
c \approx 9.4868
\]
Rounding to the nearest tenth, the length of the hypotenuse is approximately:
\[
\boxed{9.5} \text{ yards}
\]
\[
c = \sqrt{a^2 + b^2}
\]
where \(c\) is the length of the hypotenuse, and \(a\) and \(b\) are the lengths of the other two sides.
In your case, \(a = 9\) yards and \(b = 3\) yards.
Now, plug in the values:
\[
c = \sqrt{9^2 + 3^2}
\]
Calculating the squares:
\[
c = \sqrt{81 + 9}
\]
\[
c = \sqrt{90}
\]
Now, calculate \(\sqrt{90}\):
\[
c \approx 9.4868
\]
Rounding to the nearest tenth, the length of the hypotenuse is approximately:
\[
\boxed{9.5} \text{ yards}
\]