Question
A right triangle with the lengths of 30 and 90.
what is the hypotenuse?
answers:
94.6
50
9,000
what is the hypotenuse?
answers:
94.6
50
9,000
Answers
GPT-4o mini
To find the hypotenuse of a right triangle when the lengths of the other two sides (the legs) are known, you can use the Pythagorean theorem. The theorem states that in a right triangle with legs \(a\) and \(b\), and hypotenuse \(c\), the following equation holds:
\[
c^2 = a^2 + b^2
\]
In your case, the lengths of the legs are 30 and 90.
So, we calculate:
\[
c^2 = 30^2 + 90^2
\]
\[
c^2 = 900 + 8100
\]
\[
c^2 = 9000
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{9000} \approx 94.87
\]
Thus, the hypotenuse is approximately 94.87.
Among the provided options, the closest answer is **94.6**.
\[
c^2 = a^2 + b^2
\]
In your case, the lengths of the legs are 30 and 90.
So, we calculate:
\[
c^2 = 30^2 + 90^2
\]
\[
c^2 = 900 + 8100
\]
\[
c^2 = 9000
\]
Now, take the square root of both sides to find \(c\):
\[
c = \sqrt{9000} \approx 94.87
\]
Thus, the hypotenuse is approximately 94.87.
Among the provided options, the closest answer is **94.6**.