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

Explanation

yzx + 105^o + 30^o = 180^o

yzx = 180 - 155 = 45^o

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

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