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Section 6.2 Trigonometry of Right Triangles

Chapter 6 – Trigonometric Functions: Right Triangle Approach. Section 6.2 Trigonometry of Right Triangles. Definitions. In this section, we will study certain ratios of sides of right triangles, called trigonometric rations, and discuss several applications. Trigonometric Ratios.

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Section 6.2 Trigonometry of Right Triangles

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  1. Chapter 6 – Trigonometric Functions: Right Triangle Approach Section 6.2 Trigonometry of Right Triangles 6.2 - Trigonometry of Right Triangles

  2. Definitions • In this section, we will study certain ratios of sides of right triangles, called trigonometric rations, and discuss several applications. 6.2 - Trigonometry of Right Triangles

  3. Trigonometric Ratios • Consider a right triangle with  as one of its acute angles. The trigonometric ratios are as follows: 6.2 - Trigonometry of Right Triangles

  4. Examples – pg. 448 • Find the exact value of the six trigonometric ratios of the angle  in the triangle. 6.2 - Trigonometry of Right Triangles

  5. Examples – pg. 448 • Find the side labeled x. State your answer rounded to five decimal places. 6.2 - Trigonometry of Right Triangles

  6. Examples – pg. 448 • Find the side labeled x. State your answer rounded to five decimal places. 6.2 - Trigonometry of Right Triangles

  7. Special Triangles • First we will create an isosceles right triangle. Find the ratio of the sides for all 6 trig functions. 1 45 1 6.2 - Trigonometry of Right Triangles

  8. Special Triangles • Next we will create an equilateral triangle. Find the ratio of the sides for all 6 trig functions. 30 2 2 60 1 1 6.2 - Trigonometry of Right Triangles

  9. Special Triangles 6.2 - Trigonometry of Right Triangles

  10. Examples – pg. 449 • Solve the right triangle. 6.2 - Trigonometry of Right Triangles

  11. Applications • The ability to solve right triangles by using trigonometric ratios is fundamental to many problems in navigation, surveying, astronomy, and the measurement of distances. • We need to have common terminology. 6.2 - Trigonometry of Right Triangles

  12. Definitions • Line of Sight If an observer is looking at an object, then the line from the eye of the observer to the object is called the line of sight. 6.2 - Trigonometry of Right Triangles

  13. Definitions • Angle of Elevation If the object being observed is above the horizontal (plane) then the angle between the line of sight and the object is called the angle of elevation. 6.2 - Trigonometry of Right Triangles

  14. Definitions • Angle of Depression If the object being observed is below the horizontal (car) then the angle between the line of sight and the object is called the angle of depression. 6.2 - Trigonometry of Right Triangles

  15. NOTE • Angle of Inclination In many of the examples, angles of elevation and depression will be given for a hypothetical observer at ground level. If the line of sight follows a physical object, such as a plane or hillside, we use the term angle of inclination. 6.2 - Trigonometry of Right Triangles

  16. Examples – pg. 450 6.2 - Trigonometry of Right Triangles

  17. Examples – pg. 450 6.2 - Trigonometry of Right Triangles

  18. Examples – pg. 450 6.2 - Trigonometry of Right Triangles

  19. Examples – pg. 450 6.2 - Trigonometry of Right Triangles

  20. Examples – pg. 450 6.2 - Trigonometry of Right Triangles

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