2. I have faith in myself I have faith in my teachers I will accept my duties and responsibilities I will respect others and seek their respect I have self respect I have self control I can learn if I study hard I will learn because I will study hard I love myself And loving myself I'll be myself And know myself` I am the one who is talking Balance Order Harmony Reciprocity Truth Justice Righteousness Look around you And behold us in our greatness Greatness is a Panther Possibility And you can make it yours!!!!!!!!!!! SCHOOL CREED

4. Geometric Mean: (Page 342) The Positive square root of the product of two numbers. X = M M Y 3 - - 27 3 = M M 27 M 2 = 81 M = 9 9 Stated: “9 is the Geometric Mean of 3 and 27.” Chapter 7 Vocabulary

5. Geometric Mean Theorem #1: (Page 343) An altitude drawn from the vertex (right angle) of a right triangle to it’s hypotenuse divides the right triangle into 2 similar triangles. Stated:  ADB ~  BDC A BC D Chapter 7 Vocabulary

6. Geometric Mean Theorem #2: (Page 343) An altitude drawn from the vertex (right angle) of a right triangle to it’s hypotenuse is the geometric mean of the two segments of the hypotenuse A BC D Chapter 7 Vocabulary

7. Geometric Mean Theorem #3: (Page 344) An altitude drawn from the vertex (right angle) of a right triangle to it’s hypotenuse makes the measure of any leg of the triangle the geometric mean of the the measures of the entire hypotenuse and the segment of the hypotenuse adjacent to that leg. A BC D Chapter 7 Vocabulary

8. Geometric Mean Theorem #3: (Page 344) An altitude drawn from the vertex (right angle) of a right triangle to it’s hypotenuse makes the measure of any leg of the triangle the geometric mean of the the measures of the entire hypotenuse and the segment of the hypotenuse adjacent to that leg. A BC D Chapter 7 Vocabulary

9. Pythagorean Theorem: a 2 + b 2 = c 2 (Page 350) Pythagorean Triple (Page 352): Three numbers satisfying the equation a 2 + b 2 = c 2 45-45-90 SRT: The hypotenuse is radical 2 times the length of the other two equal sides. (Page 357) 30-60-90 SRT: The hypotenuse is 2 times the length of the short leg while the long leg is radical 3 times the length of the short leg. (Page 359) 45 30 60

10. Trigonometry: (Page 364) Chapter 7 Vocabulary The study of the measurement of triangles Trigonometric Ratios: (Page 364) Ratios found through the division of the lengths of the sides of a right triangle. OppositeOpposite A d j a c e n t H y p o t e n u s e AdjacentAdjacent O p p o s i t e

11. Chapter 7 Vocabulary Sine: (Page 364) The opposite side divided by the hypotenuse. 3 4 5 Sine = 3 (opposite) 5 (hypotenuse)

12. Chapter 7 Vocabulary Cosine: (Page 364) The adjacent side divided by the hypotenuse. 3 4 5 Cosine = 4 (adjacent) 5 (hypotenuse)

13. Chapter 7 Vocabulary Tangent: (Page 364) The opposite side divided by the adjacent. 3 4 5 Tangent = 3 (opposite) 4 (adjacent)

14. Chapter 7 Vocabulary Angle of Elevation: (Page 371) The angle between the line of sight and the horizontal (adjacent) side when the observer looks up.

15. Chapter 7 Vocabulary Angle of Elevation DEMO: (Page 371) What is the angle of elevation required to intercept a bird traveling the given distance at an altitude of 50 feet? 86.595 feet 50 feet Tan = 50 86.595 Tan =.5774 ~ 30 o

16. Chapter 7 Vocabulary Angle of Depression: (Page 372) The angle between the line of sight and the horizontal (adjacent) side when the observer looks down.

17. Chapter 7 Vocabulary Angle of Depression DEMO: (Page 372) What is the angle of decent of a bird traveling along a 100 foot diagonal from an altitude of 50 feet? 50 feet 100 feet Sin = 50 100 Sin =.5 = 30 o

18. Chapter 7 Vocabulary Law of Sines: (Page 377) SinA = SinB = SinC a b c A B C a b c

19. Chapter 7 Vocabulary Law of Sines (DEMO): (Page 377) SinA = SinB = SinC a b c A B C b c a 30 o What is the measure of angle B in the triangle below? Sin C = Sin B 2 4 Sin 30 o = Sin B 2 4.5 = Sin B 2 4 1 = Sin B 4 4Sin B = 4 Sin B = 1 B = 90 o

20. Chapter 7 Vocabulary Law of Cosines: (Page 385) a 2 = b 2 + c 2 – 2 (b)(c)(Cosine A) A BC a b c b 2 = a 2 + c 2 – 2 (a)(c)(Cosine B) c 2 = a 2 + b 2 – 2 (a)(b)(Cosine C)

21. Chapter 7 Vocabulary Law of Cosines (DEMO #1): (Page 385) A B C b c a 30 o What is the length of side AB in the triangle below? c 2 = a 2 + b 2 – 2 (a)(b)(Cosine C)

22. c 2 = ( ) 2 + (4) 2 – 2( )(4)(Cosine 30 o ) c 2 = 12 + 16 – (27.713)(.8660) c 2 = 12 + 16 – 24.00016 c 2 = 12 – 8.00016 c 2 = 3.9984 c = 1.999 ~ 2

23. Chapter 7 Vocabulary Law of Cosines (DEMO #2): (Page 385) A B C b c a 30 o What is the length of side AC in the triangle below? b 2 = a 2 + c 2 – 2 (a)(c)(Cosine B)

24. b 2 = ( ) 2 + (2) 2 – 2( )(2)(Cosine 90 o ) b 2 = 12 + 4 – (13.856)(0) b 2 = 12 + 4 b 2 = 16 b = 4

25. Chapter 7 Vocabulary Law of Cosines (DEMO #3): (Page 385) A B C b c a 30 o What is the length of side BC in the triangle below? a 2 = b 2 + c 2 – 2 (b)(c)(Cosine A)

26. a 2 = (4 ) 2 + (2) 2 – 2(4)(2)(Cosine 60 o ) a 2 = 16 + 4 – (16)(.5) a 2 = 16 + 4 – 8 a 2 = 16 – 4 a 2 = 12 a =

28. Tan p /2 = Sin p /2 Cos p /2 (Undefined)