In the figure, YXZ = 30°, XYZ = 105° and XY = 8cm. Calculate YZ
 

  • A 16\(\sqrt{2}\)cm
  • B 8\(\sqrt{2}\)cm
  • C 4\(\sqrt{2}\)cm
  • D 22cm
jamb 1990mathematics

The correct answer is C. 4\(\sqrt{2}\)cm

yzx + 105°+ 30°= 180°

yzx = 180 - 155 = 45°

\(\frac{yz}{sin 30^o} = \frac{8}{sin 45^o}\)

yz = \(\frac{8 \sin 30}{sin 45}\)

= 8(\(\frac{1}{2}) = \frac{8}{1} \times \frac{1}{2} \times \frac{\sqrt{2}}{1}\)

= 4 \(\div\) \(\frac{1}{\sqrt{2}}\)

= 4\(\sqrt{2}\)cm

Previous question Next question