In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of \(\overline{XY}\). Find tan (< XZT)
A
\(\frac{1}{\sqrt{3}}\)
B
\(\frac{\sqrt{3}}{2}\)
C
\(\sqrt{3}\)
D
\(\frac{1}{2}\)
Verified Correct Answer: A.
Step-by-Step Mathematical Solution
ZT = \(\sqrt{6^2 - 3^2}\)
ZT = \(\sqrt{27}\) = \(3\sqrt{3}\)
tan (< XZT) = \(\frac{3}{3\sqrt{3}}\)
= - \(\frac{1}{\sqrt{3}}\)
Source: Myschool Past Questions Archive (Record #58311)