In the figure, YXZ = 30o, XYZ = 105o and XY = 8cm. Calculate YZ
A.
16\(\sqrt{2}\)cm
B.
8\(\sqrt{2}\)cm
C.
4\(\sqrt{2}\)cm
D.
22cm
Correct answer is C
yzx + 105o + 30o = 180o
yzx = 180 - 155 = 45o
\(\frac{yz}{sin 30^o} = \frac{8}{sin 45^o}\)
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