In XYZ, y = z = 30° and XZ = 3cm. Find YZ

  • A \(\frac{\sqrt{3}}{2}\) cm
  • B 3\(\frac{\sqrt{3}}{2}\) cm
  • C 3\(\sqrt{3}\) cm
  • D 2\(\sqrt{3}\) cm
jamb 1989mathematics

The correct answer is C. 3\(\sqrt{3}\) cm

Y \(\to\) 30°

X \(\to\) 120°

Z \(\to\) 30°

\(\frac{3}{\text{sin 30}}\) = \(\frac{YZ}{\text{sin 120}}\)

YZ = \(\frac{3\times \sin 120}{\sin 30}\)

\(3 \times \frac{\sqrt{3}}{2} \times 2 = 3\sqrt{3}\)

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