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Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Chapter 8 24 Glencoe Geometry

Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a trigonometric ratio.

The three most common ratios

are sine, cosine, and tangent, which are abbreviated sin, cos, and tan, respectively. sin R = leg opposite ?R hypotenuse cos R = leg adjacent to R hypotenuse tan R = leg opposite R leg adjacent to R r t s t r s Find sin A, cos A, and tan A. Express each ratio as a fraction and a decimal to the nearest hundredth. sin A = opposite leg hypotenuse cos A = adjacent leg hypotenuse tan A = opposite leg adjacent leg BC BA AC AB BC AC 5 13 12 13 5 12

0.38 ≈ 0.92 ≈ 0.42

Exercises

Find sin

J, cos J, tan J, sin L, cos L, and tan L. Express each ratio as a fraction and as a decimal to the nearest hundredth if necessary.

1. 2. 3. 1213

5 CB A

Study Guide and Intervention

Trigonometry

8-4 st r TS R

Example

20 1216
40
2432
36

12⎷324⎷3

sin J = 12 20 = 0.6; cos J = 16 20 = 0.8; tan J = 12 16 = 0.75; sin L = 16 20 = 0.8; cos L= 12 20 0.6; tan L = 16

12 ≈ 1.33 sin J =

24
40
= 0.6; cos J = 32
40
= 0.8; tan J = 24
32
= 0.75; sin L = 32
40
= 0.8; cos L = 24
32
= 0.6; tan L = 32
24
≈ 1.33 sin J = 36

24 ⎷ ?

3 ≈ 0.87; cos J =

12 ⎷ ?

3

24 ⎷ ?

3 = 0.5; tan J = 36

12 ⎷ ?

3 ≈ 1.73; sin L =

12 ⎷ ?

3

24 ⎷ ?

3 = 0.5; cos L = 36

24 ⎷ ?

3 ≈ 0.87; tan L =

12 ⎷ ?

3 36
≈ 0.58 Copyright © Glencoe/McGraw-Hill, a division of The McGraw-Hill Compan ies, Inc.

NAME DATE PERIOD

Lesson 8-4

Chapter 8 25 Glencoe Geometry

Study Guide and Intervention (continued)

Trigonometry

Use Inverse Trigonometric Ratios You can use a calculator and the sine, cosine, or tangent to find the measure of the angle, called the inverse of the trigonometric ratio. Use a calculator to find the measure of ?T to the nearest tenth.

The measures given are those of the leg opposite

T and the hypotenuse, so write an equation using the sine ratio. sin T = opp hyp sin T = 29
34

If sin

T 29
34
, then sin 1 29
34
= m?T.

Use a calculator. So,

m T ≈ 58.5.

Exercises

Use a calculator to find the measure of

T to the nearest tenth. 1. 34

14⎷3

2. 7 18 3. 8734
4. 10132
5. 67

10⎷3

6. 39

14⎷2

8-4

Example

34
29
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