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.

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Answer 1 · 2018-05-24T02:07:43

#~~39.2\ "ft"#

By the sine law for triangles

#{XZ}/{sin /_Y} = {YZ}/{sin /_X}#

Thus we need to know #"m"/_Y#. This follows easily from

#"m"/_X+"m"/_Y+"m"/_Z = 180^circ#

and is

#"m"/_Y = 180^circ - 38^circ-67^circ = 75^circ#

Thus

# XZ = YZ times {sin /_Y}/{sin/_ X} = 25\ "ft" times {sin 75^circ}/{sin 38^circ}#

#qquad ~~ 25 times 0.9659/0.6157\ "ft" ~~39.22\ "ft"#