In triangle XYZ, ∠ XYZ = 15o, ∠ XZY = 45o and lXYl = 7 cm. Find lYZl.
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Correct Answer: Option B
Explanation:
∠ yxz = 180 - (45 + 15)
= 180 - 60
= 120o
Using sine rule
\(\frac{x}{sinx}=\frac{7}{sinz}\\
\frac{x}{sin 120}=\frac{7}{sin 45}\\
x=\frac{7 sin 120}{sin45}\\
x=\frac{7sin(180-120)}{sin 45}\\
x=\frac{7 sin 60}{sin 45}=\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\
x =\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\
x = 7\left(\frac{\sqrt{6}}{2}\right)\)
∠ yxz = 180 - (45 + 15)
= 180 - 60
= 120o
Using sine rule
\(\frac{x}{sinx}=\frac{7}{sinz}\\
\frac{x}{sin 120}=\frac{7}{sin 45}\\
x=\frac{7 sin 120}{sin45}\\
x=\frac{7sin(180-120)}{sin 45}\\
x=\frac{7 sin 60}{sin 45}=\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\
x =\left(7\left(\frac{\sqrt{3}}{2}\right)\div \frac{1}{\sqrt{2}}\right)\\
x = 7\left(\frac{\sqrt{6}}{2}\right)\)