Answer:
613.7 in
Explanation:
You want the length of side f in ∆EFG with e = 310 in, E = 27°, G = 89°.
Law of sines
The law of sines tells you ...
f/sin(F) = e/sin(E)
Angle F is the third angle in the triangle, so its measure is ...
F = 180° - 89° -27° = 64°
Then the length of f is ...
f = e·sin(F)/sin(E) = (310 in)·sin(64°)/sin(27°) ≈ 613.7 in
The length of f is about 613.7 inches.
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