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

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