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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

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Transcript of "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
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