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) Responses 123–√ 12 Start Root 3 End Root 12 12 23–√ 2 Start Root 3 End Root 6 6

Answer 1

In a 30-60-90 triangle, the sides have a specific ratio: 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 have specified the side opposite the 60-degree angle to be \( 63-\sqrt{} \). Let's denote this side as \( x\sqrt{3} \).

To find \( x \):

\[
x\sqrt{3} = 63
\]

Now, solve for \( x \):

\[
x = \frac{63}{\sqrt{3}} = 21\sqrt{3}
\]

Now, we can find the length of the hypotenuse:

\[
\text{Hypotenuse} = 2x = 2(21\sqrt{3}) = 42\sqrt{3}
\]

So, the length of the hypotenuse is \( 42\sqrt{3} \).

However, looking at your options, you have not provided any approximate choice that corresponds directly to \( 42\sqrt{3} \). So, it seems there may be a miscommunication with the terms or values provided. If you meant to give \( 63 \) without the square root, then none of the options match.

Can you please confirm the values provided for re-evaluation?