Mathematics

In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find…

In triangle XYZ, ∠XYZ = 15o, ∠XZY = 45o and lXYl = 7 cm. Find lYZl.
  • A.
    14√2 cm
  • B.
    (7left(frac{sqrt{6}}{2}right))
  • C.
    7√2 cm
  • D.
    7 cm
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(7left(frac{sqrt{3}}{2}right)div frac{1}{sqrt{2}}right)\
x =left(7left(frac{sqrt{3}}{2}right)div frac{1}{sqrt{2}}right)\
x = 7left(frac{sqrt{6}}{2}right))