# Trigonometry Law of Sines and Solving Triangles  This article covers the Law of Sines, its requirements, and how it can be used to find all sides and angles of a triangle. This is demonstrated through a sample problem involving given values for angle C, angle B, and side b.

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## About Trigonometry Law of Sines and Solving Triangles

PowerPoint presentation about 'Trigonometry Law of Sines and Solving Triangles'. This presentation describes the topic on This article covers the Law of Sines, its requirements, and how it can be used to find all sides and angles of a triangle. This is demonstrated through a sample problem involving given values for angle C, angle B, and side b.. The key topics included in this slideshow are Trigonometry, Law of Sines, triangles, angles, sides,. Download this presentation absolutely free.

## Presentation Transcript

1. 1316 Trigonometry Law of Sines Chapter 7 Sections 1&2

2. b a c B C A There is group of formulas that work for most triangles. h

3. Requirements when using the Law of Sines: You must be given two angles and any side: AAS or ASA Two sides and an angle opposite one of them: SSA OR The Law of Sines does not work for SSS or SAS

4. Find all sides and angles if C = 102.3 , B = 28.7 , and b = 27.4 feet. b a c B C A 102.3 28.7 27.4 ft 49.0

5. A pole tilts toward the sun at an angle of 8 . If it casts a 22 foot shadow and the angle of elevation from the tip of the shadow to the top of the pole is 43 , how tall is the pole? b a = ? c B C A 98 43 = 22 ft 39 shadow

6. When you are given two sides and a non-included angle (SSA) three possibilities exist You will get no triangle You will get one triangle You will get two triangles a b a b a b a b

7. Find all angles if A = 85 , a = 15, and b = 25 ft. b a c B C A 85 = 15 ft 25 ft This does not exist so there is no triangle.

8. Find all angles if A = 20.5 , a = 12, and b = 31 feet. b a c B C A 20.5 = 12 ft 31 ft This happens twice on (0 ,180 ) 64.8 94.7 20.5 44 . 3 115.2

9. Use the Law of Sines to find B : 6 8 B C 87 A With Sine there may be an angle in Quad II that also works so you must check the supplement: This is too large to be a triangle with the 87 given

10. Use the Law of Sines to find B : 3.5 4 B C 60 A Check the supplement: The data makes two triangles since both 81.8 & 98.2 work with 60

11. Use the Law of Sines to find C : 125 100 B C 67 A No triangle will be formed with these numbers.

12. Draw a triangle for each and use the Law of Sines to decide how many triangles are formed 1) B = 47 , b = 4, c = 25 No Triangle 2) C = 60, b = 30, c = 50 One Triangle 3) B = 20, a = 12, b = 5 Two triangles 4) B = 37.3, b = 12.5, c = 20.1 Two triangles 5) A = 102, a = 5, c = 12 No triangles

13. Basic Steps for working with Law of Sines Use Law of Sines with the parts you are given Draw and label a figure When you find an angle ( Sin -1 ) check if the supplement also makes a triangle Find all missing parts that are requested.