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Chapter 13

Chapter 13. Right Triangle Trigonometry. §1 3.1 – Trigonometric Ratios. Angle Initial side Terminal side Vertex. §1 3.1 – Trigonometric Ratios. Measurement Tools - Protractor. §1 3.1 – Trigonometric Ratios. Types of angles Obtuse Greater than 90 ° Acute Less than 90 °

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Chapter 13

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  1. Chapter 13 Right Triangle Trigonometry

  2. §13.1 – Trigonometric Ratios • Angle • Initial side • Terminal side • Vertex

  3. §13.1 – Trigonometric Ratios • Measurement Tools - Protractor

  4. §13.1 – Trigonometric Ratios • Types of angles • Obtuse • Greater than 90° • Acute • Less than 90° • Right • Exactly 90°

  5. §13.1 – Trigonometric Ratios • Pythagorean Theorem (Right triangles) c2 = a2 + b2

  6. §13.1 – Trigonometric Ratios • Ex: Find c in the diagram below

  7. §13.1 – Trigonometric Ratios • Ex: Find a in the diagram below

  8. §13.1 – Trigonometric Ratios • Trigonometric ratios • Relationship between an acute angle of a right triangle and the lengths of its sides • sin A = side opposite A hypotenuse • cos A = side adjacent to A hypotenuse • tan A = side opposite A side adjacent to A

  9. §13.1 – Trigonometric Ratios • Ex: Find the 3 trigonometric ratios for A

  10. §13.1 – Trigonometric Ratios • Trigonometric ratios of the otherangles • Use a calculator • Examples: • Finding the trig value given the angle • Find sin 48° • Find tan 37.25° • Finding the angle given the trig value • Find  if cos = 0.5402 • Find  if tan= 3.421

  11. §13.2 – Using Trigonometric Ratios to Find Angles • Finding the angles of a right-triangle • Must be given two sides • Must decide which trig ratio to use • Problems 13.2 #2, 4, 6 (p. 438)

  12. §13.3 – Using Trigonometric Ratios to Find Sides • Finding the sides of a right-triangle • Must be given one sides and one acute angle • Must decide which trig ratio to use • Problems 13.3 #2, 4, 6 (p. 440)

  13. §13.4 – Solving Right Triangles • Solving a triangle – Finding unknown values of sides or angles • Tools needed to solve triangles • Pythagorean theorem • Complementary angles add to 90° • Trigonometric ratios • Problems 13.4 #2, 4, 6 (p. 442)

  14. §13.5 – Applications Involving Trigonometric Ratios • Problem solving approach • Read through problem to be sure you understand what is being asked • Draw a diagram to help visualize the situation • Look for right triangles • Apply trigonometric concepts to solve the problem • Problems 13.5 #4, 8 (p. 445)

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