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The Law of Cosines

The Law of Cosines. Solve for a 2. The Law of Cosines. Use for--. SSS. SAS. Write other variations for both. + c 2. - 2 bc cos A. b 2. a 2 =. + c 2. a 2. b 2 =. - 2 ac cos B. - 2 ab cos C. + b 2. a 2. c 2 =. The Law of Cosines. Finding an Angle Using the Law of Cosines.

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The Law of Cosines

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  1. The Law of Cosines

  2. Solve for a2 The Law of Cosines Use for-- SSS SAS Write other variations for both

  3. + c2 - 2bc cos A b2 a2 = + c2 a2 b2 = - 2ac cos B - 2ab cos C + b2 a2 c2 = The Law of Cosines

  4. Finding an Angle Using the Law of Cosines Find the measure of angle A. Using the calculator: Set angle mode to degrees and enter (612 + 432 - 382) ÷ (2 x 61 x 43) = Then press: [COS-1] [ANS] [ )] [ENTER]

  5. Finding an Angle Using the Law of Cosines Given triangle DEF, find .

  6. Example 1When given 3 sides, find the largest angle first. Given a = 5, b = 8, and c =7, find all three angles. Answers B = 81.787° C = 60° A= 38.213°

  7. Applying the Law of Cosines b2 = a2 + c2 - 2ac cos B = (230)2 + (150)2 - 2(230)(150)cos 430 = 24936.59 b = 157.913 m a2 = b2 + c2 - 2bc cos A = (61)2 + (43)2 - 2(61)(43)cos 380 = 1435.09 a = 37.896 cm

  8. Example 2 Given C =111º, a =27, and b =18, find the remaining sides and angles. Answers c = 37.434 A = 42.327° B = 26.673°

  9. Example 3 A port is 50 miles due north of a lighthouse. A ship is 30 miles at a bearing of N37ºE from the lighthouse. How far is the ship from the port? Answer 31.687 miles

  10. Heron's Area Formula Need 3 sides—a, b, and c. S=1/2(perimeter)

  11. Example 4 Find the area of the triangular region with sides 50 feet, 58 feet, and 69 feet. Answer 1423.539 ft2

  12. Navigation problemp. 441 #24 A boat runs along a triangular course marked by buoys A, B, and C. The race starts with the boats headed west for 2500 meters. The other two sides of the course lie to the north of the first side, and their lengths are 1100m and 2000m. Draw a diagram and find the bearings for the last two legs of the race. Answer N 38.983°E S 64.689°E

  13. Classwork p. 441 # 2, 10, 22, 26, 29 homework p. 441 # 1,3,9,19,21,23,25,27

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