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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: = 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: = = 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 = 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 = c = 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 = c = c = 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 = c = c = 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 = c = c = 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 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 b 2 = 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 b 2 = b 2 = 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 b 2 = 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

19 Classwork 5/3: Pythagorean Theorem + Basic Trig

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

34 Classwork: Label the triangle according to the given angle

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 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 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 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 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 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 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 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 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 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 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 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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