Answer:
1. a = 34.02 and b = 10.00
2. a = 10.00 and b = 11.00
3. a = 20.00 and b = 13.98
Step-by-step explanation:
The Law of Sines is used to solve ambiguous cases which explore the case given side-side-angle informed in a triangle. Law of Sines is a relationship between in a side of a triangle and sine is the angle is opposite side.
Using the formula of Law of Sines :
- a/Sin(A) = b/Sin(B) = c/Sin(C)
1. Given : x = 180° - 127° - 25° = 28°
Solution :
- 20/Sin(28°) = a/Sin(127°) = b/Sin(25°)
Find a :
- a = 20Sin(127°)/Sin(28°)
- a = 15.97/0.469
- a = 34.02
Find b :
- b = 20Sin(25°)/Sin(28°)
- b = 8.452/0.469
- b = 10.00
2. Given : x = 180° - 108° - 38° = 34°
Solution :
- a/Sin(34°) = 17/Sin(108°) = b/Sin(38°)
Find a :
- a = 17Sin(34°)/Sin(108°)
- a = 9.506/0.951
- a = 10.00
Find b :
- b = 17Sin(38°)/Sin(108°)
- b = 10.46/0.951
- b = 11.00
3. Given : x = 180° - 23° - 34° = 123°
Solution :
- 30/Sin(123°) = a/Sin(34°) = b/Sin(23°)
Find a :
- a = 30Sin(34°)/Sin(123°)
- a = 16.77/0.838
- a = 20.00
Find b :
- b = 30Sin(23°)/Sin(123°)
- b = 11.72/0.838
- b = 13.98
