24 Glencoe Geometry Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a trigonometric ratio Study Guide and Intervention
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[PDF] Trigonometry - Study Guide and Intervention
24 Glencoe Geometry Trigonometric Ratios The ratio of the lengths of two sides of a right triangle is called a trigonometric ratio Study Guide and Intervention
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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 5 120.38 ≈ 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 AStudy Guide and Intervention
Trigonometry
8-4 st r TS RExample
20 121640
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 = 1612 ≈ 1.33 sin J =
2440
= 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 ⎷ ?
324 ⎷ ?
3 = 0.5; tan J = 3612 ⎷ ?
3 ≈ 1.73; sin L =12 ⎷ ?
324 ⎷ ?
3 = 0.5; cos L = 3624 ⎷ ?
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 = 2934
If sin
T 2934
, 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. 3414⎷3
2. 7 18 3. 87344. 10132
5. 67
10⎷3
6. 3914⎷2
8-4Example
3429
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