Answer:
d. g = 42; E = 37.7°; G = 99.3°
Step-by-step explanation:
Evaluating the problem, you find that the given angle is opposite the longest given side, so you can conclude
- there is only one solution (this is NOT an ambiguous case)
- angle E will be smaller than 43°
You can also recognize that the sum of the remaining two angles must be ...
180° -43° = 137°
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Your next step should be to look at the answer choices to check their feasibility.
a. angle E is more than 43° -- bad answer
b. sum of angles is not 137° -- bad answer
c. none -- bad answer. The triangle will have a solution.
d. sum of angles is 137°, angle E < 43° -- feasible answer
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You can further check to see if the offered choice makes sense by computing the value of angle E.
From the Law of Sines, you know that ...
sin(E)/e = sin(F)/f
sin(E) = (e/f)sin(F) . . . . . multiply by e
E = arcsin((e/f)sin(F)) ≈ 37.7° . . . . . . . . matches answer choice D
and side g will be ...
g/sin(G) = f/sin(F)
g = f(sin(G)/sin(F)) = 29(sin(137°-37.7°)/sin(43°)) ≈ 41.96
g ≈ 42.0 . . . . . . matches answer choice D
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Comment on the solution
You may have noticed we wrote the Law of Sines two ways. One used sine/side, and the other used side/sine. The particular form was chosen to put the unknown in the numerator, making it easier to solve for. Of course, with a little practice, you don't need to write the proportion. You can jump directly to the answer form you need:
- E = arcsin(e/f)sin(F))
- g = f(sin(G)/sin(F))
