Answer:
- a = 27, ∠A = 28°, ∠B = 7°
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Use the law of sines:
- a/sin ∠A = b/sin ∠B = c/sin ∠C
Use the given values and find the measure of angle B:
- 7/sin ∠B = 33/sin 145°
- sin ∠B = 7 sin 145°/33
- sin ∠B = 0.12166
- ∠B = arcsin (0.12166)
- ∠B = 7° (rounded)
We have now two angle measures.
Use triangle sum theorem to find the third angle:
- ∠A + ∠B + ∠C = 180°
- ∠A + 7° + 145° = 180°
- ∠A + 152° = 180°
- ∠A = 28°
Find the last side length:
- a/sin ∠A = b/sin ∠B
- a/sin 28° = 7/sin 7°
- a = 7 sin 28° / sin 7°
- a = 27.0 (rounded)
