For a triangle ABC, with AB=4, AC=7 and BAC^=30°, find the remaining angles.

29°, 121° or ≈ 30° and ≈ 120°

Step-by-step explanation:

Law of cosine: a² = b² + c² - 2bc cos A

a² = 16 + 49 - 2 x 4 x 7 x cos30° = 16.5

a = 4.1

Law of sin: smaller angle 4 / sin ∠BCA = 4.1 / sin 30°

sin ∠BCA = 0.49

∠BCA = 29° (≈30°)

∠ABC = 180 - 29 - 30 = 121° (≈120°)