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|
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Correct Answer: Option C
Explanation:
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,
\(\frac{PT}{RT} = \tan 60°\)
\(\frac{3\sqrt{3}}{RT} = \tan 60°\)
\(RT = \frac{3\sqrt{3}}{\sqrt{3}} = 3 cm\)
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,
\(\frac{PT}{RT} = \tan 60°\)
\(\frac{3\sqrt{3}}{RT} = \tan 60°\)
\(RT = \frac{3\sqrt{3}}{\sqrt{3}} = 3 cm\)