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

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Welcome To

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  1. Welcome To

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

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

  4. Answer Pythagorean Theorem: a2 + b2 = c2 122 + b2 = 202 144 + b2 = 400 B2 = 256 B = 16cm Back

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

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

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

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

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

  10. Answer Based on theorem 7.2, a is the geometric mean of 8 and 6, so a2 = 8*6 a2 = 48 a = 6.93 Back

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

  12. Answer Based on Theorem 7.3, AC/AB = AB/Ad So, (29+21)/(a) = (a)/(21) 50/a = a/21 a2 = 1050 a = 32.4 Back

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

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

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

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

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

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

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

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

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

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

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

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

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

  26. Answer Sin (30) = 0.5 Back

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

  28. Answer 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 Back

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

  30. Answer 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° Back

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

  32. Answer 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 Back

  33. 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?

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

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

  36. Answer A Back

  37. 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?

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

  39. 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?

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

  41. 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?

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

  43. The Laws of Sines and Cosinesfor $100 Write out the law of sines

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

  45. The Laws of Sines and Cosinesfor $200 Write out the law of cosines

  46. Answer Law of cosines: A2 = B2 + C2 – 2BC*cos(a) B2 = A2 + C2 – 2AC*cos(b) C2 = A2 + B2 – 2AB*cos(c) Back

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

  48. Answer 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° Back

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

  50. Answer B2 = A2 + C2 – 2AC*cos(b) B2 = 102 + 52 – 2(10)(5)*cos(40) B2 = 125 – 100cos(40) B2 = 48.396 B = 7 Back

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