# Trigonometry Short Questions (Question 4 - 6)

Question 4:

In the diagram above, WZY  is a straight line.  and WZ = XZ = 30 cm. Find the length of XY.

Solution:
$\begin{array}{l}\angle WXZ=\angle XWZ={30}^{o}\\ \therefore \angle XZY={30}^{o}+{30}^{o}={60}^{o}\\ \\ \mathrm{sin}\angle XZY=\frac{XY}{XZ}\\ \mathrm{sin}{60}^{o}=\frac{XY}{30}\\ XY=\mathrm{sin}{60}^{o}×30\\ XY=25.98cm\end{array}$

Question 5:

In the diagram above, PQS is a right angle triangle. Given that SR = 6cm, PQ = 12 cm and 5SR = 2PS. Find the value of cos α and tan β.

Solution:

Question 6:

In the diagram above, ADC is a straight line, if  . Find the distance of AC.

Solution: