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Trig Functions of Acute Angles. Lesson 2.2. A. c. b. B. C. a. Right Triangle Ratios. Given a right triangle Ratios. Right Triangle Ratios. Given a specific triangle determine the ratios How to find the hypotenuse? Use the Pythagorean theorem Ratios. 7. 5. B.

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right triangle ratios

A

c

b

B

C

a

Right Triangle Ratios
  • Given a right triangle
  • Ratios
right triangle ratios3
Right Triangle Ratios
  • Given a specific triangledetermine the ratios
  • How to find the hypotenuse?
    • Use the Pythagorean theorem
  • Ratios

7

5

B

right triangle ratios4
Right Triangle Ratios
  • Note: Text suggests importance of memorizing table on pg. 137 …
  • Consider instead memorizing some standard triangles and deriving table as needed
right triangle ratios5
Right Triangle Ratios
  • Some important relationships for standard triangles

30°

45°

2

2

1

45°

60°

60°

1

1

1

reciprocal trig functions
Reciprocal Trig Functions
  • Secant
  • Cosecant
  • Cotangent
  • Note: newer models of calculators will have these built in
    • Older systems can create functions
    • Older TI-89's may be updated
evaluating trig expressions
Evaluating Trig Expressions
  • Use calculator
  • Important to keep track of when calculator is in radian or degree mode
  • Use 2nd D to have function evaluate with degrees, even when in radian mode
exercises for 2 2a
Exercises for 2.2A
  • Page 142
  • 1 – 49 EOO
solving triangles
Solving Triangles
  • For now problem will involve right triangles
  • Usually one side and one angle will be given
    • Must find one or both of the other sides

Distance acrossthe water?

  • Ask which trig ratio?
  • Write equation
  • Solve for unknown quantity

52°

31 m

solving triangles10
Solving Triangles
  • Some problems talk about angle of elevation
    • The line of sight above the horizontal
  • The angle of depression
    • The line of sight below the horizontal
solving triangles11
Solving Triangles
  • Ask which trig ratio?
  • Write equation
  • Solve for unknown quantity
  • Find the height of an object by measuring distances and the angle of elevation

The angle of elevation is 37.5°

76.89 ft

Experiment with Elevation Spreadsheet

exercises for 2 2b
Exercises for 2.2B
  • Page 143
  • Exercises53, 54, 57, 60, 63, 65,