In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
A
14√2 cm
B
\(7\left(\frac{\sqrt{6}}{2}\right)\)
C
7√2 cm
D
7 cm
Verified Correct Answer: B.
Step-by-Step Mathematical Solution
∠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\(\left(\frac{\sqrt{6}}{2}\right)\)
Source: Myschool Past Questions Archive (Record #8836)