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First, we need to find the third angle ∠A by using the formula:
∠A = 180° - ∠C - ∠B
∠A = 180° - 32° - ∠B
Now, we can use the Law of Sines to find the possible values for angles and sides. The Law of Sines states:
a/sin∠A = b/sin∠B = c/sin∠C
1. Using the given information:
a/sin∠A = 45/sin∠C
a/sin∠A = 45/sin(32°)
a/sin∠A = 45/sin(32°)
a/sin∠A = 45/0.5299
a/sin∠A ≈ 84.9
2. Using the side b:
b/sin∠B = 45/sin∠C
47/sin∠B = 45/sin(32°)
47/sin∠B = 45/0.5299
47/sin∠B ≈ 51.4
Now, we can find the possible values for angles and sides:
∠A1 = sin^(-1)(84.9*sin(32°)/47) ≈ 57.0°
∠A2 = 180° - ∠A1 ≈ 123.0°
∠B1 = sin^(-1)(47*sin(32°)/45) ≈ 31.0°
∠B2 = 180° - ∠B1 ≈ 149.0°
a1 ≈ 84.9
a2 ≈ 84.9