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What do we call one of these? Solve!

Lesson: _____ Section 6.1 The Law of Sines. What do we call one of these? Solve! What does it mean when we say that two quantities are proportional?. The Law of Sines. C. b. a. h. A. B. applet. The Law of Sines. C. a. b. - or -. B. A. c.

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What do we call one of these? Solve!

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  1. Lesson: _____ Section 6.1The Law of Sines • What do we call one of these? • Solve! • What does it mean when we say that two quantities are proportional?

  2. The Law of Sines C b a h A B applet

  3. The Law of Sines C a b - or - B A c ex. B=110°, C=30, c=10.5, Solve the triangle!

  4. Law of Sines Law of Cosines Solving Oblique (non-right) Triangles We need three pieces of information, one of which must be a side. 4 cases are possible… 1.) 2 angles and any side 2.) 2 sides and an angle opposite one of the sides 3.) 3 sides 4.) 2 sides and their included angle

  5. The Law of SinesAMBIGUOUS CASE (SSA) Three possible situations can occur • No such triangle exists • Exactly 1 triangle fits the description • Two different triangles both fit the description What does “ambiguous” mean? Why is this called the “ambiguous” case? Examples 3,4,5 from the text are good. Ex.4.(No solutions): a = 15, b = 25, A = 85° Ex.3.(1 solution): a = 22, b = 12, A = 42°Ex.5.(2 solutions): a = 12, b = 31, A = 20.5°

  6. If we are dealing with the SSA case (Ambiguous), Use the Law of Sines to solve for . Then set up 2 cases to represent both the acute case  and the obtuse case (180 - ). Draw a diagram for each of these cases. After solving each triangle, test to see that everything is ok. Do the angles add to 180? Is the side-angle relationship preserved?

  7. C a h b B A c Area of an Oblique Triangle Formula Area = ½ bc sinA = ½ ab sinC = ½ ac sinB This is the same as Area = ½ bhShow why!

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