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งาȨณิตศาสตร์อาจารย์๶ค

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krookay2012
krookay2012

This document contains examples of using the Pythagorean theorem to solve for the lengths of sides of right triangles. It provides two examples: 1) For a right triangle with sides of lengths 9, 12, and c, it uses the Pythagorean theorem (c^2 = 9^2 + 12^2) to calculate that c = 15. 2) For a right triangle with sides of lengths 11, 60, and c, it uses the Pythagorean theorem (c^2 = 11^2 + 60^2) to calculate that c = 61.

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งาȨณิตศาสตร์อาจารย์๶ค
1.1 ABC ABC B A C
AB AC BC 2 2 2 C = A B
1 ABC C B C 15 A 8 C
2 C 2 2 = 8 + 15 = 64 + 225 = 289 = 17 x 17 = 17 C = 17 17
2 b 1. b 2 2 2 2 2 2 2 = 1. 2 + b b = 2 - 1.2
= 2.56 = 1.6 x 1.6 b = 1.6 1.6 1.1 1.
1. 9 ,12 2. 11,60 2. 24 20 12 1. 7 2.
3 12 1. 15 61 2.11
1. 9,12 2 2 2 C = 12 + 9 = 144 + 81 = 225 2 = 15 x 15 C = 15 15
2. 11, 60 C = 60 + 11 = 3,600 + 121 = 3,721 = 61 x 61 C = 61 61
1. 20 12 2 2 2 2 a = c + b 2 a = 16 a = 20 + 12 16 2 = 400 - 144 = 256
2. 7 24 2 2 2 C = 7+ 24 = 49 + 576 = 625 = 25 x 25 2 C = 25 25
12 1. 15 2 2 2 2 B = c - b B = 9 = 15 - 12 9 = 225 - 144 = 81
2. 11 61 2 2 2 A = c - b 60 = 61 - 11 = 3,721 -121 = 3,600 2 = 60 x 60 A = 60
13 1
=
A c b B a C 2 2 2 ABC AB = C BC = a AC = b c = a + b
DEF EF D DF a b b DFE E a F
2 2 2 DEF DE = a + b 2 2 2 ABC 2 c = a +b 2 DE = c ~ DE = c DEF = ABC . . . DFE = ACB = 90
Pythagoras of Samos 580 -496
55 Crotona
a b
งาȨณิตศาสตร์อาจารย์๶ค
a b
a b a 2.25 4 9.00 8 1 0 1. 9 8 9 4 2 0 = 2.250… 2 0 4
5 9 1. = 0.555… 7 15 0.5 2. 50 = 0.4666… 33 0.46 11 37 3. - = - 1.515151… -1.51
1 4 1. 0.20 0.30 2.650 -1.83520 2. 1.18 , -2.327
11 100 1 . 0.11= 137 1,000 2. - 0.137 =
1 0.6 N = 0.6 N = 0.666… 1 1 x 10 1 x 10 10 1 2 10 N - N = 10 x
2 10 2 1 - 10 N = 6.666… + 0.666… 9N = 6 2 N =6 1 9 0.6 = 6 2 9 3
2 0.725 N = 0.725 1 N = 0.7252525… 1 x 1,000 2 1,000 N = 1000 x 0.7252525 1000 N =
1 x 10 10 N = 10 x 0.7252525 … 3 10 N = 7.252525 --- 10 2 - 3 1000N - 10N = 725.2525… - 7.2525… 990N =
N = 718 990 0.725… = 718 990 718 990
งาȨณิตศาสตร์อาจารย์๶ค
2.2 a b a b b =0 1.23456789101121314… 3.4323223222…
งาȨณิตศาสตร์อาจารย์๶ค
งาȨณิตศาสตร์อาจารย์๶ค
2.3 a a a
7 49 7 = 49 -7 49 -7 = 49 a a
225 225 = 3x3x 5x5 2 = 5x 3 x 5x3 = 15 x
a a a
= =- =- -
N = N = x ; n = x n = x ; n = x
– ; n- n = ( )– ( ) n = n = =
= = = =
= =- = - -
= = =
= = = = =
= x ax + b = 0 a,b a≠0
x+ = x- - x (- x) x = (- x) x- (- )x = (- )x - - x = - - x+ – =- – - x=- - - x - = - - x=
x x = x– ( x ) =( x )- = - = x = x-
x= x x x= x( x ) x= x x x= x=
x x = x x =( x ) x = = x= x
- y = (p- ) = p – (y - )– ( y) = x - (x - ) = - x
- -
งาȨณิตศาสตร์อาจารย์๶ค
- x x x– - x (x - ) =- x x- =- (x x)- =- x - =- x =-
- - - = - (- ) (- )=- - - - -
x x,x x x (x ) (x ) = x x x = (x x x) ( ) = x = x = x =
, = = ,
-
งาȨณิตศาสตร์อาจารย์๶ค
- ,- - -
งาȨณิตศาสตร์อาจารย์๶ค
= =
งาȨณิตศาสตร์อาจารย์๶ค
งาȨณิตศาสตร์อาจารย์๶ค
งาȨณิตศาสตร์อาจารย์๶ค
=
งาȨณิตศาสตร์อาจารย์๶ค
AE = DF
AE = DF
งาȨณิตศาสตร์อาจารย์๶ค
งาȨณิตศาสตร์อาจารย์๶ค
MB = NT
X
MB = NT X= X=

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งาȨณิตศาสตร์อาจารย์๶ค

  • 2. 1.1 ABC ABC B A C
  • 3. AB AC BC 2 2 2 C = A B
  • 4. 1 ABC C B C 15 A 8 C
  • 5. 2 C 2 2 = 8 + 15 = 64 + 225 = 289 = 17 x 17 = 17 C = 17 17
  • 6. 2 b 1. b 2 2 2 2 2 2 2 = 1. 2 + b b = 2 - 1.2
  • 7. = 2.56 = 1.6 x 1.6 b = 1.6 1.6 1.1 1.
  • 8. 1. 9 ,12 2. 11,60 2. 24 20 12 1. 7 2.
  • 9. 3 12 1. 15 61 2.11
  • 10. 1. 9,12 2 2 2 C = 12 + 9 = 144 + 81 = 225 2 = 15 x 15 C = 15 15
  • 11. 2. 11, 60 C = 60 + 11 = 3,600 + 121 = 3,721 = 61 x 61 C = 61 61
  • 12. 1. 20 12 2 2 2 2 a = c + b 2 a = 16 a = 20 + 12 16 2 = 400 - 144 = 256
  • 13. 2. 7 24 2 2 2 C = 7+ 24 = 49 + 576 = 625 = 25 x 25 2 C = 25 25
  • 14. 12 1. 15 2 2 2 2 B = c - b B = 9 = 15 - 12 9 = 225 - 144 = 81
  • 15. 2. 11 61 2 2 2 A = c - b 60 = 61 - 11 = 3,721 -121 = 3,600 2 = 60 x 60 A = 60
  • 16. 13 1
  • 17. =
  • 18. A c b B a C 2 2 2 ABC AB = C BC = a AC = b c = a + b
  • 19. DEF EF D DF a b b DFE E a F
  • 20. 2 2 2 DEF DE = a + b 2 2 2 ABC 2 c = a +b 2 DE = c ~ DE = c DEF = ABC . . . DFE = ACB = 90
  • 21. Pythagoras of Samos 580 -496
  • 22. 55 Crotona
  • 23. a b
  • 25. a b
  • 26. a b a 2.25 4 9.00 8 1 0 1. 9 8 9 4 2 0 = 2.250… 2 0 4
  • 27. 5 9 1. = 0.555… 7 15 0.5 2. 50 = 0.4666… 33 0.46 11 37 3. - = - 1.515151… -1.51
  • 28. 1 4 1. 0.20 0.30 2.650 -1.83520 2. 1.18 , -2.327
  • 29. 11 100 1 . 0.11= 137 1,000 2. - 0.137 =
  • 30. 1 0.6 N = 0.6 N = 0.666… 1 1 x 10 1 x 10 10 1 2 10 N - N = 10 x
  • 31. 2 10 2 1 - 10 N = 6.666… + 0.666… 9N = 6 2 N =6 1 9 0.6 = 6 2 9 3
  • 32. 2 0.725 N = 0.725 1 N = 0.7252525… 1 x 1,000 2 1,000 N = 1000 x 0.7252525 1000 N =
  • 33. 1 x 10 10 N = 10 x 0.7252525 … 3 10 N = 7.252525 --- 10 2 - 3 1000N - 10N = 725.2525… - 7.2525… 990N =
  • 34. N = 718 990 0.725… = 718 990 718 990
  • 36. 2.2 a b a b b =0 1.23456789101121314… 3.4323223222…
  • 39. 2.3 a a a
  • 40. 7 49 7 = 49 -7 49 -7 = 49 a a
  • 41. 225 225 = 3x3x 5x5 2 = 5x 3 x 5x3 = 15 x
  • 42. a a a
  • 43. = =- =- -
  • 44. N = N = x ; n = x n = x ; n = x
  • 45. – ; n- n = ( )– ( ) n = n = =
  • 47. = =- = - -
  • 48. = = =
  • 49. = = = = =
  • 50. = x ax + b = 0 a,b a≠0
  • 51. x+ = x- - x (- x) x = (- x) x- (- )x = (- )x - - x = - - x+ – =- – - x=- - - x - = - - x=
  • 52. x x = x– ( x ) =( x )- = - = x = x-
  • 53. x= x x x= x( x ) x= x x x= x=
  • 54. x x = x x =( x ) x = = x= x
  • 55. - y = (p- ) = p – (y - )– ( y) = x - (x - ) = - x
  • 56. - -
  • 58. - x x x– - x (x - ) =- x x- =- (x x)- =- x - =- x =-
  • 59. - - - = - (- ) (- )=- - - - -
  • 60. x x,x x x (x ) (x ) = x x x = (x x x) ( ) = x = x = x =
  • 61. , = = ,
  • 62. -
  • 64. - ,- - -
  • 66. = =
  • 70. =
  • 77. X
  • 78. MB = NT X= X=