To solve the problem, we first need to recognize the properties of a 30-60-90 triangle. In a 30-60-90 triangle, the sides are proportional in the following way:
- The side opposite the 30° angle is the shortest side and is denoted as [tex]\( x \)[/tex].
- The side opposite the 60° angle is [tex]\( x\sqrt{3} \)[/tex].
- The hypotenuse, which is the side opposite the 90° angle, is [tex]\( 2x \)[/tex].
Given:
- One angle measures 60°.
- The shortest side (opposite the 30° angle) measures [tex]\( 3 \sqrt{3} \)[/tex] inches.
Since the shortest side is opposite the 30° angle in a 30-60-90 triangle, we can set [tex]\( x = 3 \sqrt{3} \)[/tex].
Using the side ratios of a 30-60-90 triangle:
- The hypotenuse is [tex]\( 2x \)[/tex].
Thus, we find the hypotenuse by plugging in the value of [tex]\( x \)[/tex]:
[tex]\[ \text{Hypotenuse} = 2 \times 3 \sqrt{3} \][/tex]
To further simplify:
[tex]\[ \text{Hypotenuse} = 6 \][/tex]
Therefore, the length of the hypotenuse of the triangle is:
[tex]\[ \boxed{6} \][/tex]
So the correct answer is:
C. 6
