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Trigonometric Ratios  in Right Triangles
Trigonometric Ratios  are based on the Concept of  Similar Triangles!
All 45º- 45º- 90º Triangles are Similar! 45 º 2  2  45 º 1  1  45 º 1
All 30º- 60º- 90º   Triangles are Similar! 1 ½ 2 4 60º  30º 60º  30º 2 60º  30º 1
All 30º- 60º- 90º   Triangles are Similar! 10 60º  30º 5 2 60º  30º 1 1 60º  30º
A triangle in which one angle is a right angle is called a  right triangle .  The side opposite the right angle is called ...
Naming Sides of Right Triangles  Hypotenuse  Side Adjacent  Side Opposite  
The Tangent Ratio There are a total of six ratios that can be made with the three sides.  Each has a specific name.  Side...
The Six Trigonometric Ratios (The SOHCAHTOA model) S  O  H  C  A  H  T  O  A  Side Adjacent   Hypotenuse Side Opposite  
The Six Trigonometric Ratios The Cosecant, Secant, and Cotangent of     are the Reciprocals of  the Sine, Cosine,and Tang...
Reciprocal Identities Quotient Identities
 
Find the value of each of the six trigonometric functions of the angle  Adjacent 12 13 c  = Hypotenuse = 13 b   = Opposite...
 
25 h h  = 23.49
Solving a Problem with the Tangent Ratio 60º  53 ft h = ? We know the angle and the  side adjacent to 60º.  We want to  kn...
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Right triangle trigonometry Slide 1 Right triangle trigonometry Slide 2 Right triangle trigonometry Slide 3 Right triangle trigonometry Slide 4 Right triangle trigonometry Slide 5 Right triangle trigonometry Slide 6 Right triangle trigonometry Slide 7 Right triangle trigonometry Slide 8 Right triangle trigonometry Slide 9 Right triangle trigonometry Slide 10 Right triangle trigonometry Slide 11 Right triangle trigonometry Slide 12 Right triangle trigonometry Slide 13 Right triangle trigonometry Slide 14 Right triangle trigonometry Slide 15 Right triangle trigonometry Slide 16
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Right triangle trigonometry

  1. 1. Trigonometric Ratios in Right Triangles
  2. 2. Trigonometric Ratios are based on the Concept of Similar Triangles!
  3. 3. All 45º- 45º- 90º Triangles are Similar! 45 º 2 2 45 º 1 1 45 º 1
  4. 4. All 30º- 60º- 90º Triangles are Similar! 1 ½ 2 4 60º 30º 60º 30º 2 60º 30º 1
  5. 5. All 30º- 60º- 90º Triangles are Similar! 10 60º 30º 5 2 60º 30º 1 1 60º 30º
  6. 6. A triangle in which one angle is a right angle is called a right triangle . The side opposite the right angle is called the hypotenuse , and the remaining two sides are called the legs of the triangle. c b a
  7. 7. Naming Sides of Right Triangles  Hypotenuse  Side Adjacent Side Opposite 
  8. 8. The Tangent Ratio There are a total of six ratios that can be made with the three sides. Each has a specific name.  Side Adjacent  Hypotenuse Side Opposite  Tangent  
  9. 9. The Six Trigonometric Ratios (The SOHCAHTOA model) S O H C A H T O A  Side Adjacent  Hypotenuse Side Opposite 
  10. 10. The Six Trigonometric Ratios The Cosecant, Secant, and Cotangent of  are the Reciprocals of the Sine, Cosine,and Tangent of   Side Adjacent  Hypotenuse Side Opposite 
  11. 11. Reciprocal Identities Quotient Identities
  12. 13. Find the value of each of the six trigonometric functions of the angle Adjacent 12 13 c = Hypotenuse = 13 b = Opposite = 12
  13. 15. 25 h h = 23.49
  14. 16. Solving a Problem with the Tangent Ratio 60º 53 ft h = ? We know the angle and the side adjacent to 60º. We want to know the opposite side. Use the tangent ratio: Why? 1 2
  • MorganGardner13

    Dec. 9, 2021
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    Jan. 23, 2020
  • justinjean

    Jan. 21, 2020
  • CevOctobre

    Feb. 20, 2018
  • luisamonteroalves

    Feb. 28, 2012

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