To solve the question, let's first understand the type of right triangle we're dealing with.
Given:
- The shortest side of the right triangle measures [tex]\(3 \sqrt{3}\)[/tex] inches.
- One angle of the triangle measures [tex]\(60^\circ\)[/tex].
We recognize that this is a 30-60-90 triangle. In a 30-60-90 triangle, the sides have a specific ratio:
- The side opposite the 30° angle (the shortest side) is [tex]\(x\)[/tex].
- The side opposite the 60° angle (the longer leg) is [tex]\(x\sqrt{3}\)[/tex].
- The hypotenuse (opposite the right angle) is [tex]\(2x\)[/tex].
Here, the given shortest side [tex]\(x\)[/tex] measures [tex]\(3 \sqrt{3}\)[/tex] inches. According to the ratio:
- The hypotenuse is [tex]\(2x\)[/tex].
Let's calculate the length of the hypotenuse:
[tex]\[ \text{Hypotenuse} = 2 \times (3\sqrt{3}) = 6 \sqrt{3} \][/tex]
So, the length of the hypotenuse of the triangle is [tex]\(6 \sqrt{3}\)[/tex] inches.
Thus, the correct answer is:
C. [tex]\(6 \sqrt{3}\)[/tex]
