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6.5: The Law of Cosines

6.5: The Law of Cosines. TSW be able to apply the Law of Cosines to solve triangles, and be able to apply Heron’s Formula to find the area of a triangle at an 85% mastery level as demonstrated by discussion and practice. A. b. c. C. B. a. The Law of Cosines.

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6.5: The Law of Cosines

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  1. 6.5: The Law of Cosines TSW be able to apply the Law of Cosines to solve triangles, and be able to apply Heron’s Formula to find the area of a triangle at an 85% mastery level as demonstrated by discussion and practice.

  2. A b c C B a The Law of Cosines In any triangle ABC, we have

  3. Length of a Tunnel A tunnel is to be built through a mountain. To estimate the length of the tunnel, a surveyor makes the measurements shown. Use the surveyor’s data to approximate the length of the tunnel. A B 82.4o 212 ft 388 ft C

  4. SSS Ex: The sides of a triangle are a = 5, b = 8, and c = 12. Find the angles of the triangle. SAS (use both Laws)

  5. Navigation A pilot sets out from an airport and heads in the direction N20oE, flying at 200 mi/h. After one hour, he makes a course correction and heads in the direction N40oE. Half an hour after that, engine trouble forces him to make an emergency landing. a. Find the distance between the airport and his final landing point. b. Find the bearing from the airport to his final landing point.

  6. Area: Heron’s Formula

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