In the diagram, XYZ is an equilateral triangle of side 6cm and Y is the midpoint of \(\overline{XY}\). Find tan (< XZT)
-
\(\frac{1}{\sqrt{3}}\)
- \(\frac{\sqrt{3}}{2}\)
- \(\sqrt{3}\)
- \(\frac{1}{2}\)
The correct answer is: A
Explanation
ZT = \(\sqrt{6^2 - 3^2}\)
ZT = \(\sqrt{27}\) = \(3\sqrt{3}\)
tan (< XZT) = \(\frac{3}{3\sqrt{3}}\)
= - \(\frac{1}{\sqrt{3}}\)