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In the diagram, QRT is a straight line. If angle PTR = 90°, angle PRT…

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)