Question on: JAMB Mathematics - 1990

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
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Correct Option: 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

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