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\(\theta\)
Attached Figure / Diagram
A
\(\frac{3}{5}\)
B
\(\frac{1}{2}\)
C
\(\frac{2}{5}\)
D
\(\frac{1}{5}\)
Verified Correct Answer: D.
Step-by-Step Mathematical Solution
\(\frac{5}{\sin 30^o} = \frac{2}{\sin \theta} = \frac{5}{\frac{1}{2}} = \frac{2}{\sin \theta}\)
10 = \(\frac{2}{\sin \theta}\)
sin\(\theta\) = \(\frac{2}{10}\)
= \(\frac{1}{5}\)
Source: Myschool Past Questions Archive (Record #33071)