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In the figure, YXZ = 30^o, XYZ = 105^o a...

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

A.

16 $\sqrt{2}$ cm

B.

8 $\sqrt{2}$ cm

C.

4 $\sqrt{2}$ cm

D.

22cm

View answer & explanation

Correct answer is C

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

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