3. $100 $200 $300 $400 $500 $200 $300 $400 $500 Geometric mean Pythagorean Thm. Special Right Triangles Law of Sines and Cosines Trigonometry Angles of elevation and depression

4. Geometric Mean and the Pythagorean Theorem for $100 Solve for b: 12cm 20cm b

5. Answer Pythagorean Theorem: a 2 + b 2 = c 2 12 2 + b 2 = 20 2 144 + b 2 = 400 B 2 = 256 B = 16cm Back

6. Geometric Mean and the Pythagorean Theorem $200 Find the geometric mean between 32 and 2

7. Answer x = √(32*2) = √(64) = 8 Back

8. Geometric Mean and the Pythagorean Theorem for $300 List three Pythagorean triples

9. Answer Answers may vary: 3,4,5 6,8,10 5,12,13 20,48,52 Back

10. Geometric Mean and the Pythagorean Theorem for $400 Solve for a

11. Answer Back Based on theorem 7.2, a is the geometric mean of 8 and 6, so a 2 = 8*6 a 2 = 48 a = 6.93

12. Geometric Mean and the Pythagorean Theorem for $500 In triangle ABC, solve for the length of a

13. Based on Theorem 7.3, AC/AB = AB/Ad So, (29+21)/(a) = (a)/(21) 50/a = a/21 a 2 = 1050 a = 32.4 Answer Back

14. Special Right Triangles for $100 Draw and label the sides of a 45-45-90 right Triangle

15. Answer 45-45-90 Right Triangle: Back x x√(2) x 90°45°

16. Special Right Triangles for $200 Draw and label the sides of a 30-60-90 right Triangle

17. Answer 30-60-90 Right Triangle Back x 2x x√(3) 60° 30° 90°

18. Special Right Triangles for $300 If in triangle ABC, AB = 10, BC = 12 and CA = 9, which angle has the greatest measure?

19. Answer Angle A has the greatest measure because it is opposite side BC, which is the longest side. Back

20. Special Right Triangles for $400 Solve for x and y

21. Answer Back Since the triangle is a 30-60-90, 30√(2) = 2y x = y√(3) y = 15√(2) x = 15√(2)√(3) x = 15√(6)

22. Special Right Triangles for $500 Solve for x and y

23. Answer Back Since the triangle is a 45-45-90 y = 7 (isosceles triangle so the legs are the same length) x = 7√(2)

24. Trigonometry for $100 List the three basic trigonometry functions and what they equal

25. Sin (x) = opposite hypotenuse Cos (x) = adjacent hypotenuse Tan (x) = opposite adjacent Answer Back

26. Trigonometry for $200 Evaluate: Sin (30)

27. Answer Back Sin (30) = 0.5

28. Trigonometry for $300 Evaluate cos(x): 15 25 20 90°x°

29. 15 is the adjacent side to x 20 is the side opposite of x 25 is the length of the hypotenuse Cos(x) = adjacent/hypotenuse So, cos(x) = (15/25) = 3/5 Answer Back

30. Trigonometry for $400 Solve for x: 12 22 90° x°

31. We are given the opposite (12) and the adjacent (22) sides to x, so we will use tangent. Since we are solving for the angle, we use tan -1 tan -1 (12/22) = x x = 28.6° Answer Back

32. Trigonometry for $500 Write the ratios for sin(x) and cos(x)

33. Triangle XYZ is a right triangle, so the trig functions apply From angle X, √(119) is the opposite side 5 is the adjacent side 12 is the hypotenuse sin(x) = opp/hyp = √(119)/12 cos(x) = adj/hyp = 5/12 Answer Back

34. Angles of Elevation and Depression for $100 A person is standing at point A looking at point B. Does this represent an angle of elevation or depression?

35. Answer Back Angle of depression because they are looking down from the horizontal

36. Angles of Elevation and Depression for $200 Draw an example of an angle of elevation. Label the angle A

37. Answer Back A

38. Angles of Elevation and Depression for $300 A person stands at the top of the tower and looks down at their friend who is standing 18yds from the base of the tower. If the angle of depression is 30 degrees, how tall is the tower?

39. Answer Back Tan(30) = x/18 18*tan(30) = x x = 10.4 yds

40. Angles of Elevation and Depression for $400 An airplane over the Pacific sights an atoll at an angle of depression of 5. At this time, the horizontal distance from the airplane to the atoll is 4629 meters. What is the height of the plane to the nearest meter?

41. Answer Back tan(5) = x/4629m 4629*tan(5) = x x = 405m

42. Angles of Elevation and Depression for $500 To find the height of a pole, a surveyor moves 140 feet away from the base of the pole and then measures the angle of elevation to the top of the pole to be 44. To the nearest foot, what is the height of the pole?

43. Answer Back 140 ft. x 44° tan(44) = x/140 140*tan(44) = x 135ft = x

44. The Laws of Sines and Cosines for $100 Write out the law of sines

45. Answer Back The law of sines: Sin(A) = Sin(B) = Sin(C) a b c

46. The Laws of Sines and Cosines for $200 Write out the law of cosines

47. Answer Back Law of cosines: A 2 = B 2 + C 2 – 2BC*cos(a) B 2 = A 2 + C 2 – 2AC*cos(b) C 2 = A 2 + B 2 – 2AB*cos(c)

48. The Laws of Sines and Cosines for $300 In triangle ABC, AB = 8, BC = 12 and the m<A = 62 degrees. Solve for m<C. A 62° B C 8 12

49. Sin(A) = Sin(B) = Sin(C) a b c Sin(62) = Sin(C) 12 8 8(.0735789661) = sin(c) sin -1 (.5886) = c c = 36.06° Answer Back

50. The Laws of Sines and Cosines for $400 In triangle ABC, AB = 5, BC = 10 and the m<B = 40 degrees. Solve for AC. A 40° B 5 10 C

51. Answer Back B 2 = A 2 + C 2 – 2AC*cos(b) B 2 = 10 2 + 5 2 – 2(10)(5)*cos(40) B 2 = 125 – 100cos(40) B 2 = 48.396 B = 7

52. The Laws of Sines and Cosines for $500 In triangle ABC, AB = 8, BC = 6 and the AC = 13. Solve for m<A. A B 8 6 C 13

53. Answer Back A 2 = B 2 + C 2 – 2BC*cos(a) 6 2 = 13 2 + 8 2 – 2(13)(8)*cos(a) 36 = 233 – 208cos(a) -197 = -208cos(a) 0.9471 = cos (a) cos -1 (0.9471) = a a = 18.7°