1. Page 622 1)
a ≈ , B ≈ 125°, C ≈ 35° 3)
c ≈ , B ≈ °, C ≈ ° 5)
a ≈ , B ≈ °, C ≈ ° 7)
c ≈ , B ≈ °, C ≈ ° 9)
A ≈ 120°, B ≈ °, C ≈ °
11)
A ≈ °, B ≈ °, C ≈ °
13)
A ≈ °, B ≈ °, C ≈ °
15)
A ≈ °, B ≈ °, C ≈ °
19)
≈ km
21)
≈ ft
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10.2: Law of Sines

2. Pre-Calculus AB PreAP/Dual, Revised ©2014
Law of Sines
Section 10.2
Pre-Calculus AB PreAP/Dual, Revised ©2014
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10.2: Law of Sines

3. Proof
Consider the following triangle, ABC inscribed in a circle with the center of O and the radius of r.
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10.2: Law of Sines

4. Law of Sines Can be applied with AAS, ASA, or SSA triangles
With AAS and ASA problems, the proportion can be applied (Two Angles with one side)
SSA triangles involve the ambiguous case when the angle is not the included
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10.2: Law of Sines

5. Steps Draw the figure and label the missing parts of the shape
Identify the type of triangle and the missing sides
If the triangle is AAS or ASA, apply the proportion (if two angles are given)
If the triangle is SSA, the ambiguous case must be applied
Compare the side that is given in relation to the angle to the other side
If it is GREATER than, the possibilities is that it is ONE SOLUTION
If it is LESS than, the possibilities is that it is either NO SOLUTION or TWO SOLUTIONS
Make sure the answer is in degree mode
Round answers to 4 decimal places
Check
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10.2: Law of Sines

6. Example 1 Solve for b when a = 42.9 cm., A = 32, and B = 81.8°
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10.2: Law of Sines

7. Could you solve this using Law of Cosines?
Solve for b when a = 42.9 cm., A = 32, and B = 81.8°
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10.2: Law of Sines

8. Example 2 Solve for c when a = 10 ft, B = 36°, and C = 39°
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10.2: Law of Sines

9. Your Turn Solve for a when c = 15 meters, A = 33°, and B = 119°
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10.2: Law of Sines

10. Ambiguous Case Possibilities of SSA cases
If the triangle is SSA, the ambiguous case must be applied
Compare the side that is given in relation to the angle to other side
If it is GREATER than, the possibilities is that it is ONE SOLUTION
If it is LESS than, the possibilities is that it is either NO SOLUTION or TWO SOLUTIONS
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10.2: Law of Sines

11. Ambiguous Case
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10.2: Law of Sines

12. Demo
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10.2: Law of Sines

13. Think of when Law of Sines…
If the first is bigger, then shoot the trigger. (1 triangle) If the first is less, then it is a mess. (0 or 2 triangles)
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10.2: Law of Sines

14. Example 3 Solve for C when a = 10.7, c = 7.2, and A = 43.5°
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10.2: Law of Sines

15. Example 3 Solve for C when a = 10.7, c = 7.2, and A = 43.5°
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10.2: Law of Sines

16. Example 4 Solve for A when a = 25.1, b = 8.94, and B = 55°
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10.2: Law of Sines

17. Example 5 Solve for B when a = 22.8, b = 24.9, and A = 55.3°
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10.2: Law of Sines

18. Example 5 Solve for B when a = 22.8, b = 24.9, and A = 55.3°
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10.2: Law of Sines

19. Your Turn Solve for B when a = 12 cm., b = 15 cm., and A = 40°
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10.2: Law of Sines

20. Example 6
Alyssa is taking a walk along a straight road. She decides to leave the road so she walks on a path that makes an angle of 35° with the road. After walking 450 meters, she turns 75° and heads back towards the road. How far does she need to walk on her current path to get back to the road?
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10.2: Law of Sines

21. Example 7
A blimp is seen over Austin, Texas at the same time by 2 observers that are 12 miles from one another on Congress Street. If the observers are on opposite sides of the blimp and the angles of elevation of the observers to the blimp are 28° and 37°, find the height of the blimp. Round to four decimal places.
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10.2: Law of Sines

22. Example 7
A blimp is seen over Austin, Texas at the same time by 2 observers that are 12 miles from one another on Congress Street. If the observers are on opposite sides of the blimp and the angles of elevation of the observers to the blimp are 28° and 37°, find the height of the blimp. Round to four decimal places.
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10.2: Law of Sines

23. Assignment Page 634 1-7 odd, 17-25 odd (omit 23), 41, 43
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10.2: Law of Sines