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8.1.1 – Introduction to Law of Sines /Cosines

8.1.1 – Introduction to Law of Sines /Cosines. All triangles we have dealt with to this point involve only right triangles Certainly, we have other types of triangles that will occur in real life and math purposes What other types of triangles could we have?.

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8.1.1 – Introduction to Law of Sines /Cosines

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  1. 8.1.1 – Introduction to Law of Sines/Cosines

  2. All triangles we have dealt with to this point involve only right triangles • Certainly, we have other types of triangles that will occur in real life and math purposes • What other types of triangles could we have?

  3. To help deal with the new situation, we will introduce two laws which will assist us in certain situations • Law of Sines = used for two situations, similar to geometry properties: • 1) Two angles and a side (AAS or ASA) • 2) Two sides and a non-included angle (SSA)

  4. Law of Sines, Cont’d • The Law of Sines may be written as:

  5. The Law of Sinesmay also be written as:

  6. To use the law of sines, we must know at least 2 sides and a corresponding angle, or be able to determine other angle measures using basic geometry principles

  7. Example. An air balloon is floating according to the diagram illustrated below. Find the length to the “A” marker.

  8. Example. You are trying to determine the height of an unknown tree, but the tree is growing at an angle of 83 degrees with respect to the ground. Standing from 45 feet away, the angle to see the top of the tree is 20 degrees. Find the height of the tree.

  9. Example. You are playing pool, and hit the cue ball off the edge at a 100 degree angle. The ball stops 22 inches away with a 15 degree angle from where it started. How far did the ball travel (total)?

  10. Example. Coach Jones is riding on an obstacle course. He rides 26 feet to the first obstacle, then must turn at 100 degrees to make the next one. He rides another 14 feet, before seeing he would have to turn about 56 degrees to make it back to the original point. Find the distance back to the starting spot.

  11. Assignment • Pg. 610 • 2, 4, 5, 6, 11, 12

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