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Lesson 9.9 Introduction To TrigonometryPowerPoint Presentation

Lesson 9.9 Introduction To Trigonometry

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### Lesson 9.9 Introduction To Trigonometry

Objective:

After studying this section, you will be able to understand three basic trigonometric relationships

This section presents the three basic trigonometric ratios sine, cosine, and tangent.

The concept of similar triangles and the Pythagorean Theorem can be used to develop trigonometry of right triangles

Consider the following 30-60-90 triangles

Compare the length of the leg opposite the 30 angle with the length of the hypotenuse in each triangle.

J

E

B

k = 6

f = 4

h = 3

d = 2

c = 2

a = 1

A

H

D

C

F

K

e =

j =

b =

By using similar triangles, we can see that in every 30-60-90 triangle

Engineers and Scientist have found it convenient to formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Example 1 formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Find:

a.

b.

B

c

5

C

A

12

Example 2 formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Find the three trigonometric ratios for angles A and B

B

5

3

C

A

4

Example 3 formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Triangle ABC is an isosceles triangle, find sin C

A

13

13

B

C

10

Example 4 formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Use the fact that tan 40 is approximately 0.8391 to find the height of the tree to the nearest foot.

h

50 ft

40

Summary formalize these relationships by naming the ratios of sides. You should memorize these three basic ratios.

Summarize in your own words how to find the sin, cos, and tangent of a 30-60-90 triangle.

Homework:

Worksheet 9.9

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