Question

what is the length of the hypotenuse of a 30 - 60 - 90 triangle if the side opposite the 60 - degree angle is ( 6sqrt{3} )? (1 point)
6
12
( 12sqrt{3} )
( 2sqrt{3} )

Explanation:

Step1: Recall the ratio of sides in 30 - 60 - 90 triangle

In a 30 - 60 - 90 triangle, if the side opposite 30° is \(x\), the side opposite 60° is \(x\sqrt{3}\), and the hypotenuse is \(2x\).

Step2: Find the value of \(x\)

Given the side opposite 60° is \(6\sqrt{3}\). Since the side opposite 60° is \(x\sqrt{3}\), we have \(x\sqrt{3}=6\sqrt{3}\). Solving for \(x\), divide both sides by \(\sqrt{3}\), so \(x = 6\).

Step3: Calculate the hypotenuse

The hypotenuse is \(2x\). Substitute \(x = 6\) into \(2x\), we get \(2\times6=12\).

Answer:

12