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5.4 Law of Cosines

5.4 Law of Cosines.  Law of Sines. ASA or AAS SSA What’s left??? Law of Cosines.  Law of Sines (always thinking about “ambiguous case”). … SAS and SSS. Which one to use?? whichever is appropriate. Ex 1) Solve △ ABC if m ∠ C = 79 ° , a = 25 and b = 29. B. Have SAS Find c

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5.4 Law of Cosines

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  1. 5.4 Law of Cosines

  2.  Law of Sines ASA or AAS SSA What’s left??? Law of Cosines  Law of Sines (always thinking about “ambiguous case”) … SAS and SSS Which one to use?? whichever is appropriate

  3. Ex 1) Solve △ABC if m∠C = 79°, a = 25and b = 29 B Have SAS Find c (Law of Cosines) 25 c 34.5 79° C A 29 Use Law of Sines Now, m∠A (or m∠B … doesn’t really matter which one) m∠B = 180 – 79 – 45.3 = 55.7° A = 45.3°

  4. Ex 2) Solve △ABC if a = 14.3, b = 10.6and c = 8.4 B Divide class into 3 different groups Each group solves the △ in a different order 14.3 8.4 C A 10.6 • Group 1 • m∠A (law of cos) • m∠B • m∠C • Group 2 • m∠B (law of cos) • m∠A • m∠C • Group 3 • m∠C (law of cos) • m∠A • m∠B law of sines law of sines law of sines

  5. Ex 2) Solve △ABC if a = 14.3, b = 10.6and c = 8.4 B 14.3 8.4 Each group will list their answers C A 10.6 • Group 1 • m∠A = 96.9° • m∠B = 47.4° • m∠C = 35.7° • Group 2 • m∠A = 83.4° • m∠B = 47.4° • m∠C = 35.7° • Group 3 • m∠A = 83.4° • m∠B = 47.4° • m∠C = 35.7° Total = 180° Total = 166.5° Total = 166.5° Add them up! WHAT!?! Who is right? Only Group 1 is right… why? What is unique about their situation that made them get the right answers but the rest of us didn’t? So… if we have SSS, what’s the best order to solve them?

  6. “Heading” is used in navigation The degree measure is calculated differently than in the rest of math Math: Heading: go counter-clockwise go clockwise start (due N) start

  7. Ex 3) Two airplanes leave an airport at the same time. The heading of the first is 150º and the heading of the second is 260º. If the planes travel at the rates of 680 mi/h and 560 mi/h, respectively, how far apart are they after 2 hours? Plane I (150°): 10° Plane II (260°): 150° 80° 260° 30° 1120 B A 110° 1360 b b = 2036 mi C

  8. Homework #504 Pg 269 #12, 14, 21, 24, 25, 27, 28, 29, 33, 35 Answers to Evens: 59.7 539.3 ft 3203 miles 28) 20 nautical miles #24 & 25: When a pilot changes the heading, redraw the axes at that location

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