In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT = 60°, angle PQR = 30° and |PQ| = (6sqrt{3}cm), calculate |RT|
-
A.
0.3cm -
B.
(frac{sqrt{3}}{2}cm) -
C.
3cm -
D.
(3sqrt{3}cm)
Correct Answer: Option C
Explanation
In (Delta) QPT,
(frac{PT}{6sqrt{3}} = sin 30°)
PT = (6sqrt{3} times frac{1}{2} = 3sqrt{3} cm)
In (Delta) RPT,
(frac{PT}{RT} = tan 60°)
(frac{3sqrt{3}}{RT} = tan 60°)
(RT = frac{3sqrt{3}}{sqrt{3}} = 3 cm)