Round to the nearest tenth.

  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

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

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: