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

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

Correct Answer: Option C

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