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9-3 Law of Sines

9-3 Law of Sines. Law of Sines. B. Given an oblique triangle (no right angle) we can draw in the altitude from vertex B Label the altitude k and find two equations involving k. c. k. a. A. b. C. Law of Sines.

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9-3 Law of Sines

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  1. 9-3 Law of Sines

  2. Law of Sines B • Given an oblique triangle (no right angle) we can draw in the altitude from vertex B • Label the altitude k and find two equations involving k c k a A b C

  3. Law of Sines • By using the equations for the area of a triangle. We can obtain the equation for the Law of Sines by dividing everything by

  4. Law of Sines • In triangle ABC the following is true • What are we given? • AAS or ASA Two angles and any side (1 possible triangle) • SSATwo sides and an angle opposite from one of them (ambiguous case: may not be a solution, 1 or 2 solutions)

  5. EXAMPLE #1 • A civil engineer wants to determine the distances from points A and B to an inaccessible point C. From direct measurement the engineer knows that AB=25m, <A=110°, and <B=20°. Find AC and BC. C a b 110° 20° B A 25m

  6. EXAMPLE #2 • In triangle RST, <S=126°, s=12, and t=7. Determine whether <T exists. If so, find all possible measures of <T.

  7. Example #3 • Solve triangle RST is <S=40°, r=30, and s=20. Give angle measure to the nearest tenth of a degree and lengths to the nearest hundredth.

  8. Example #4 • Solve triangle ABC when <C=112°, c=5, and a=7.

  9. Example #4 • Solve triangle ABC when <A=30°, a=7, and c=16.

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