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Warm-Up: May 20, 2013

Refresh your geometry knowledge by learning how to prove triangle congruence and applying the Law of Sines to solve trigonometric problems. Understand the relationships between angle measures and side lengths in triangles.

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Warm-Up: May 20, 2013

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  1. Warm-Up: May 20, 2013 Think back to geometry. Write down the ways to prove that two triangles are congruent.

  2. The Law of Sines

    Section 6.1
  3. The Law of Sines For a triangle with angle measures A, B, C and side lengths opposite those angles of a, b, c: True for any triangle (acute, right, obtuse)
  4. Solving a Triangle Solving a triangle means finding all side lengths and angle measures Use Law of Sines A+B+C=180˚ For examples, you-try’s and homework, round side lengths and angle measures to 3 decimal places. Law of Sines can be used to solve a triangle if 2 angles and 1 side are known (SAA or ASA) or two sides and an angle opposite one of them (SSA)
  5. Solving a Triangle: SAA or ASA Start by drawing a rough sketch of a triangle (not to scale) Find the third angle measure (A+B+C=180˚) Use Law of Sines twice to find the two missing side lengths Draw a better version of your triangle (to scale) Check that your longest side is across from biggest angle, shortest side is across from smallest angle
  6. Example 1: SAA Solve the triangle
  7. You-Try #1: SAA Solve the triangle
  8. Example 2: ASA Solve the triangle
  9. You-Try #2: ASA Solve the triangle
  10. Assignments Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
  11. Warm-Up: May 21, 2013 Find all angles θ in the interval [0, 2π) such that
  12. Homework Questions?
  13. SSA: The Ambiguous Case Given two side lengths and an angle opposite one of them, there could be 0, 1, or 2 triangles
  14. SSA: How Many Triangles? Assume a, b, and A are given If , then there are no triangles If , then there is one right triangle If , then there are two triangles If , then there is one triangle The Law of Sines will give you the number of triangles
  15. Example 3: SSA Solve the triangle
  16. Example 4: SSA Solve the triangle
  17. Example 5: SSA Solve the triangle
  18. You-Try #5: SSA Solve the triangle
  19. Assignments Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
  20. Warm-Up: May 22, 2013 Solve the triangle (hint: there are two solutions)
  21. Homework Questions?
  22. Area of an Oblique Triangle An oblique triangle is one that does not contain a right angle Area is one half the product of the length of two sides and the sine of the included angle
  23. Example 6: Area Find the area of a triangle with the following measurements
  24. You-Try #6: Area Find the area of a triangle with the following measurements
  25. Assignments Page 607 #1-13 Every Other Odd Page 608 #17-29 Every Other Odd Page 608 #33-45 Every Other Odd
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