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.

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