Question

In △XYZ , m∠X=38∘ , m∠Z=67∘ , and YZ=25 feet . What is XZ ? Enter your answer as a decimal in the box. Round only your final answer to the nearest tenth.

Answer 1

39.2

Explanation:

According to law of sines, sin(A)/a = sin(B)/b = sin(C)/c

then we have: sin(X)/YZ = sin(Y)/XZ

Y = 180 - 38 - 67 = 75

=> sin(X)/YZ = sin(Y)/XZ

sin(38)/25 = sin(75)/XZ

XZ = sin(75)/[sin(38)/25]

XZ = 25[sin(75)/[sin(38)]

XZ = 25(0.96592583/0.61566148)

XZ = 39.22 or 39.2

Answer 2

Using the law of the sine we have:
x / sine (m∠Y) = 25 / sine (m∠X)
Where,
m∠Y = 180 - m∠X - m∠Z
m∠Y = 180 - 38 - 67
m∠Y = 75
Substituting values:
x / sine (75) = 25 / sine (38)
Rewriting we have:
x = (25 / sine (38)) * (sine (75))
x = 39.22309033
Round to the nearest tenth
x = 39.2 feet
Answer:
XZ = 39.2 feet