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3 May 2011 no clickers Algebra 2. Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles*

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Presentation on theme: "3 May 2011 no clickers Algebra 2. Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles*"— Presentation transcript:

1 3 May 2011 no clickers Algebra 2

2 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles* Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

3 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles* Example: Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

4 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles* Example: 6 2 + 8 2 = 10 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

5 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 *only true for right triangles* Example: 6 2 + 8 2 = 10 2 36 + 64 = 100 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

6 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

7 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 6 2 + 10 2 = c 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

8 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 6 2 + 10 2 = c 2 36 + 100 = c 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

9 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 6 2 + 10 2 = c 2 36 + 100 = c 2 136 = c 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

10 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 6 2 + 10 2 = c 2 36 + 100 = c 2 136 = c 2  c = Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

11 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 6 2 + 10 2 = c 2 36 + 100 = c 2 136 = c 2  c = = Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

12 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

13 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 5 2 + b 2 = 13 2 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

14 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 5 2 + b 2 = 13 2 25 + b 2 = 169 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

15 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 5 2 + b 2 = 13 2 25 + b 2 = 169-25 b 2 = 144 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

16 Pythagorean Thm & Basic Trig 5/3 Pythagorean Theorem Pythagorean Theorem: a 2 + b 2 = c 2 5 2 + b 2 = 13 2 25 + b 2 = 169 b 2 = 144  b = 12 Mathematics.PPF.602: (28-32) Use the Pythagorean theorem

17 Student Practice Label a sheet of paper “Classwork 5/3: Pythagorean Theorem + Basic Trig” Complete questions 1-5 from the next slide

18 Classwork 5/3: Pythagorean Theorem + Basic Trig 1.2. 3. 4. 5.

19 Classwork 5/3: Pythagorean Theorem + Basic Trig 1.2. 3. 4. 5.

20 Pythagorean Thm & Basic Trig 5/3 Basic Trig Trigonometry (Trig) is based on three ratios: sine, cosine, tangent. In order to find these ratios, we need to be able to label a triangle’s three sides. Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

21 Pythagorean Thm & Basic Trig 5/3 Basic Trig Opposite Side A The opposite side is the side farthest away from the given angle (A) Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

22 Pythagorean Thm & Basic Trig 5/3 Basic Trig Hypotenuse A The hypotenuse is the longest side of the triangle Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

23 Pythagorean Thm & Basic Trig 5/3 Basic Trig Adjacent A Side The adjacent side is the shorter side touching the given angle (A) Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

24 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

25 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Opposite Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

26 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Hypotenuse Opposite Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

27 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Adjacent Hypotenuse Opposite Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

28 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

29 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Opposite Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

30 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Opposite Hypotenuse Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

31 Pythagorean Thm & Basic Trig 5/3 Basic Trig Label the triangle based on the given angle: Opposite Hypotenuse Adjacent Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

32 Student Practice Continue on your classwork page Complete questions 6-14 from the next slide

33 Classwork: Label the triangle according to the given angle. 6. 7. 8. 9. 10. 11. 12. 13. 14.

34 Classwork: Label the triangle according to the given angle. 6. 7. 8. 9. 10. 11. 12. 13. 14.

35 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Opposite Hypotenuse Adjacent A Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

36 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Opposite Hypotenuse Adjacent A Sine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

37 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Opposite Hypotenuse Adjacent A Sine(A) = Cosine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

38 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Opposite Hypotenuse Adjacent A Sine(A) = Cosine(A) = Tangent(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

39 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find sine (A) A 4 5 3 Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

40 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find sine (A) A 4 5 3 sine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

41 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find sine (A) A 4 5 3 sine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

42 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find cosine (A) A 4 5 3 Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

43 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find cosine (A) A 4 5 3 cosine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

44 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find cosine (A) A 4 5 3 cosine(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

45 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find tangent (A) A 4 5 3 Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

46 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find tangent (A) A 4 5 3 tangent(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

47 Pythagorean Thm & Basic Trig 5/3 Trig Ratios Given angle A, find tangent (A) A 4 5 3 tangent(A) = Mathematics.FUN.502: (24-27) Express the sine, cosine, and tangent of an angle in a right triangle as a ratio of given side lengths

48 Student Practice Continue on your classwork page Complete questions 15-20 from the next slide For each triangle, find sine, cosine and tangent for the given angle.

49 Student Practice Continue on your classwork page Complete questions 15-20 from the next slide For each triangle, find sine, cosine and tangent for the given angle Example: (B)sine B = = cosine B = = tangent B = =

50 Student Practice 15. (A)16. (A) 17. (Z)18.(Y) 19.(B)

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