Right triangle trigonometry

Right triangle trigonometry

• 1.
  Trigonometric Ratios in Right Triangles
• 2.
  Trigonometric Ratios are based on the Concept of Similar Triangles!
• 3.
  All 45º- 45º-90º Triangles are Similar! 45 º 2 2 45 º 1 1 45 º 1
• 4.
  All 30º- 60º-90º Triangles are Similar! 1 ½ 2 4 60º 30º 60º 30º 2 60º 30º 1
• 5.
  All 30º- 60º-90º Triangles are Similar! 10 60º 30º 5 2 60º 30º 1 1 60º 30º
• 6.
  A triangle inwhich 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.
  Naming Sides ofRight Triangles  Hypotenuse  Side Adjacent Side Opposite 
• 8.
  The Tangent RatioThere 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.
  The Six TrigonometricRatios (The SOHCAHTOA model) S O H C A H T O A  Side Adjacent  Hypotenuse Side Opposite 
• 10.
  The Six TrigonometricRatios The Cosecant, Secant, and Cotangent of  are the Reciprocals of the Sine, Cosine,and Tangent of   Side Adjacent  Hypotenuse Side Opposite 
• 11.
  Reciprocal Identities QuotientIdentities
• 12.
   
• 13.
  Find the valueof each of the six trigonometric functions of the angle Adjacent 12 13 c = Hypotenuse = 13 b = Opposite = 12
• 14.
   
• 15.
  25 h h = 23.49
• 16.
  Solving a Problemwith 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