Question
What is the length of the hypotenuse of a 30-60-90 triangle if the side opposite the 60-degree angle is 63–√ ?(1 point)Responses123–√12 Start Root 3 End Root23–√2 Start Root 3 End Root6612
Answers
GPT-4o mini
In a 30-60-90 triangle, the side lengths have a specific ratio: the length of the side opposite the 30-degree angle is \(x\), the side opposite the 60-degree angle is \(x\sqrt{3}\), and the hypotenuse is \(2x\).
In this case, you mentioned that the side opposite the 60-degree angle is \(63\sqrt{3}\).
From the ratio:
\[
x\sqrt{3} = 63\sqrt{3}
\]
To find \(x\), we can divide both sides by \(\sqrt{3}\):
\[
x = 63
\]
Now, to find the hypotenuse, which is given by \(2x\):
\[
\text{Hypotenuse} = 2x = 2 \times 63 = 126
\]
Thus, the length of the hypotenuse is \(126\).
It looks like the options provided don't include \(126\), so please double-check the side lengths or the answers provided. If you need to follow through the answers given, it seems there may have been a misunderstanding or miscommunication in the triangle side setup.
In this case, you mentioned that the side opposite the 60-degree angle is \(63\sqrt{3}\).
From the ratio:
\[
x\sqrt{3} = 63\sqrt{3}
\]
To find \(x\), we can divide both sides by \(\sqrt{3}\):
\[
x = 63
\]
Now, to find the hypotenuse, which is given by \(2x\):
\[
\text{Hypotenuse} = 2x = 2 \times 63 = 126
\]
Thus, the length of the hypotenuse is \(126\).
It looks like the options provided don't include \(126\), so please double-check the side lengths or the answers provided. If you need to follow through the answers given, it seems there may have been a misunderstanding or miscommunication in the triangle side setup.