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

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

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