Question

3. Two triangles can be formed with the given information. Use the Law of Sines to solve the triangles.

A = 55°, a = 12, b = 14 (1 point)
B = 72.90, C = 52.1°, C = 12.5; B = 107.1°, C = 17.9°, C = 12.5
B = 72.90, C = 52.1°, C = 11.6; B = 107.1°, C = 17.9°, c = 4.5
B = 17.1°, C = 107.9°, C = 10.3; B = 162.99, C = 72.1°, c = 10.3
B = 17.1°, C = 107.9°, C = 13.9; B = 162.99, C = 72.1°, C = 13.9

Answer 1

9514 1404 393

Answer:

(b) B = 72.90, C = 52.1°, C = 11.6; B = 107.1°, C = 17.9°, c = 4.5

Explanation:

Sometimes, the best way to answer a multiple-choice question is to see which choices are self-consistent.

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Side lengths and their opposite angle measures in a triangle have the same ordering, least to greatest. It is informative to look at the answer choices with this in mind.

1a. C < A < B; a < c < b . . . . inconsistent

2a. C < A < B; c < a < b.

2b. C < A < B; c < a < b . . . . consistent

3a. B < A < C; c < a < b . . . . inconsistent

4a. B < A < C; a < c < b . . . . inconsistent

Only answer choice 2 is self-consistent. It is the correct one.