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Warm-Up: May 20, 2013

Warm-Up: May 20, 2013. Think back to geometry. Write down the ways to prove that two triangles are congruent. The Law of Sines. Section 6.1. The Law of Sines. For a triangle with angle measures A, B, C and side lengths opposite those angles of a, b, c:

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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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