Name: Date: Similarity: Trigonometric Ratios

[Pages:3]Name:____________________

Date:_______________

Similarity: Trigonometric Ratios

We already know that any right triangle with a given acute angle is similar to every other

right triangle with that same acute angle measure (AA Postulate).

We can use the AA Postulate to discover properties of the

A D

angles in the triangle:

Example: CD intersects right triangle, ABC. Identify

whether ABC~CBD~ACD

C

B

Notice that CBD and ACD are also right triangles

C

ABC ~ ACD because of AA: m A = m A; m C = m D. ABC ~ CBD because of AA: m B = m B; m D = m C A D CBD ~ ACD because of AA: m C = m C; m D = m D

Therefore, ABC~CBD~ACD

C

A

B

D

C

B

Trigonometric ratios are established ratios used to find the acute angle measures in right triangles. For example, to find the m A in ABC above, apply the trigonometric ratio, sine, to compare the values of opposite leg a to hypotenuse c.

Sin A = CB/AB

If the measurement of a is unknown, use cosine to compare the values of the adjacent leg to

the hypotenuse: Cos A = AC/CB

A summary of these ratios, their shortenings (how they appear on your calculator), and the values they compare are listed below. Note that theta () is a Greek symbol used to represent the unknown angle.

Trigonometric Ratio Sine

Cosine

Shortening sin

cos

Values Compared

Opposite leg Hypotenuse

Adjacent Leg Hypotenuse



Name:____________________

Practice. Identify the sine or cosine.

1.sin =

A

6

C

24 B

3. sin =

8

Date:_______________

2. cos =

A

C A

4. Sin =

10

8

3

B

6

C

5

B

5. cos = 12

24

6. sin =

A

25 15

C

B

7. sin =

A

32

8. cos =

8

4

9. cos =

C

B

15

20

10. sin =

36

27



Name:____________________

Answer Key

Date:_______________

Similarity: Trigonometric Ratios

1. sin = ? 2. cos = 3/8 3. sin = 3/5 4. sin = 10/52 = 22 5. cos = 22 6. sin = 15/25 = 3/5 7. sin = 3/32 = 2/2 8. cos = ? 9. cos = 4/5 10. sin = 4/5



 ................
................

In order to avoid copyright disputes, this page is only a partial summary.

Google Online Preview   Download