1. Right Triangle Trigonometry
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
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 other angles
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 =
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)