In the figure YXZ 30o XYZ 105o and XY 8cm Calcu... - JAMB Mathematics 1990 Question
A
16\(\sqrt{2}\)cm
B
8\(\sqrt{2}\)cm
C
4\(\sqrt{2}\)cm
D
22cm
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
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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