Answer:
Step-by-step explanation:
Since this is a 30-60-90 triangle, we need the Pythagorean triple for such a triangle. the side length across from the 30 degree angle is labeled as x, the side across from the 60 degree angle is x√3, and the hypotenuse is 2x. Since we know the side length of the side across from the 60 degree angle, we use that identity and solve for x:
[tex]x\sqrt{3}=18[/tex] and
[tex]x=\frac{18}{\sqrt{3} }[/tex] and rationalizing the denominator,
[tex]x=\frac{18}{\sqrt{3} }*\frac{\sqrt{3} }{\sqrt{3} }=\frac{18\sqrt{3} }{3}=6\sqrt{3}[/tex]
This is the side length of the side across from the 30 degree angle. In order to find the hypotenuse, we have to multiply this value by 2 to get
12√3, the third choice down.
