In XYZ, y = z = 30^\circ and XZ = 3cm. Find YZ
A
\(\frac{\sqrt{3}}{2}\) cm
B
3\(\frac{\sqrt{3}}{2}\) cm
C
3\(\sqrt{3}\) cm
D
2\(\sqrt{3}\) cm
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
Y \(\to\) 30^\circ
X \(\to\) 120^\circ
Z \(\to\) 30^\circ
\(\frac{3}{\text{sin 30}}\) = \(\frac{YZ}{\text{sin 120}}\)
YZ = \(\frac{3\times \sin 120}{\sin 30}\)
\(3 \times \frac{\sqrt{3}}{2} \times 2 = 3\sqrt{3}\)
Source: Myschool Past Questions Archive (Record #31585)