In the diagram, QRT is a straight line. If angle PTR = 90^\circ, angle PRT = 60^\circ, angle PQR = 30^\circ and |PQ| = \(6\sqrt{3}cm\), calculate |RT|
Attached Figure / Diagram
A
0.3cm
B
\(\frac{\sqrt{3}}{2}cm\)
C
3cm
D
\(3\sqrt{3}cm\)
Verified Correct Answer: C.
Step-by-Step Mathematical Solution
In \(\Delta\) QPT,
\(\frac{PT}{6\sqrt{3}} = \sin 30^\circ\)
PT = \(6\sqrt{3} \times \frac{1}{2} = 3\sqrt{3} cm\)
In \(\Delta\) RPT,
\(\frac{PT}{RT} = \tan 60^\circ\)
\(\frac{3\sqrt{3}}{RT} = \tan 60^\circ\)
\(RT = \frac{3\sqrt{3}}{\sqrt{3}} = 3 cm\)
Source: Myschool Past Questions Archive (Record #26558)