In the figure, XYZ is a triangle with XY = 5cm, XZ = 2cm and XZ is produced to E making the angle < YZE = 150o. If the angle XYZ = \(\theta\), calculate the value of sin\(\theta\)
A.
\(\frac{3}{5}\)
B.
\(\frac{1}{2}\)
C.
\(\frac{2}{5}\)
D.
\(\frac{1}{5}\)
Correct answer is D
\(\frac{5}{\sin 36^o} = \frac{2}{\sin \theta} = \frac{5}{\frac{1}{2}} = \frac{2}{\sin \theta}\)
10 = \(\frac{2}{\sin \theta}\)
sin\(\theta\) = \(\frac{2}{10}\)
= \(\frac{1}{5}\)