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 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. Naming Sides of Right Triangles  Hypotenuse  Side Adjacent Side Opposite 

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. The Six Trigonometric Ratios (The SOHCAHTOA model) S O H C A H T O A  Side Adjacent  Hypotenuse Side Opposite 

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. Reciprocal Identities Quotient Identities

13. Find the value of each of the six trigonometric functions of the angle Adjacent 12 13 c = Hypotenuse = 13 b = Opposite = 12

15. 25 h h = 23.49

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