In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = \(6\sqrt{3}cm\), calculate |RT|

In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = \(6\sqrt{3}cm\), calculate |RT|

A.

0.3cm

B.

\(\frac{\sqrt{3}}{2}cm\)

C.

3cm

D.

\(3\sqrt{3}cm\)

Correct answer is C

In \(\Delta\) QPT,

\(\frac{PT}{6\sqrt{3}} = \sin 30°\)

PT = \(6\sqrt{3} \times \frac{1}{2} = 3\sqrt{3} cm\)

In \(\Delta\) RPT,

\(\frac{PT}{RT} = \tan 60°\)

\(\frac{3\sqrt{3}}{RT} = \tan 60°\)

\(RT = \frac{3\sqrt{3}}{\sqrt{3}} = 3 cm\)