1. Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Check Skills You’ll Need
(For help, go to Lesson 8-3.)
For each triangle, find (a) the length of the leg opposite B and (b) the length of the leg adjacent to B. 1. 3. 2.
Check Skills You’ll Need
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2. b. The leg adjacent to B is the one that is a side of the angle: 12.
Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Check Skills You’ll Need
1. a. The leg opposite B is the one that is not a side of the angle: 9.
b. The leg adjacent to B is the one that is a side of the angle: 12.
2. a. The leg opposite B is the one that is not a side of the angle: 7.
b. The leg adjacent to B is the one that is a side of the angle:
3. a. The leg opposite B is the one that is not a side of the angle: 10.
b. The leg adjacent to B is the one that is a side of the angle:
Solutions
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3. Use the figure for Exercises 1–3.
The Tangent Ratio
May 9, 2003
Lesson 8-3
Lesson Quiz
Use the figure for Exercises 1–3.
1. Write the tangent ratio for K.
2. Write the tangent ratio for M.
3. Find m M to the nearest degree. 15 8 8 15 28
Find x to the nearest whole number. 4. 5. 52 29
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4. Textbook

5. Textbook

6. Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Notes
One way to describe the relationship of sine and cosine is to say that sin x = cos(90 - x) for values of x between 0 and 90.
This type of equation is called an identity because it is true for all the allowed values of the variable.
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7. Writing Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Additional Examples
Writing Sine and Cosine Ratios
Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms.
sin G = = 16 20 4 5
opposite
hypotenuse
cos T = = 16 20 4 5
adjacent
hypotenuse
cos G = = 12 20 3 5
adjacent
hypotenuse
sin T = = 12 20 3 5
opposite
hypotenuse
Quick Check
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8. Real-World Connection
Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Additional Examples
Real-World Connection
A 20-ft. wire supporting a flagpole forms a 35˚ angle with the flagpole. To the nearest foot, how high is the flagpole?
The flagpole, wire, and ground form a right triangle with the wire as the hypotenuse.
Because you know an angle and the measures of its adjacent side and the hypotenuse, you can use the cosine ratio to find the height of the flagpole.
cos 35° =
height 20
Use the cosine ratio.
height = 20 • cos 35°
Solve for height.
Use a calculator.
The flagpole is about 16 ft tall.
Quick Check
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9. Using the Inverse of Sine and Cosine
Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Additional Examples
Using the Inverse of Sine and Cosine
A right triangle has a leg 1.5 units long and hypotenuse 4.0 units long. Find the measures of its acute angles to the nearest degree.
Draw a diagram using the information given.
Use the inverse of the cosine function to find m A.
cos A =
1.5
4.0
0.375 =
Use the cosine ratio.
Use the inverse of the cosine.
m A = cos–1(0.375)
Use a calculator.
Round to the nearest degree.
m A 68
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10. Definition of complementary angles
Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Additional Examples
(continued)
To find m B, use the fact that the acute angles of a right triangle are complementary.
m A + m B = 90
Definition of complementary angles
Substitute.
68 + m B
m B
The acute angles, rounded to the nearest degree, measure 68 and 22.
Quick Check
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11. Use this figure for Exercises 1 and 2.
Sine and Cosine Ratios
May 9, 2003
Lesson 8-4
Lesson Quiz
Use this figure for Exercises 1 and 2.
1. Write the ratios for sin A and sin B.
2. Write the ratios for cos A and cos B.
sin A = or , sin B = or 16 34 30 8 17 15
cos A = or , cos B = or 16 34 30 15 17 8
Use this figure for Exercises 3 and 4.
3. Find x to the nearest tenth.
4. Find y to the nearest tenth.
21.0
13.6
Use this figure for Exercises 5 and 6.
5. Find x to the nearest degree.
6. Find y to the nearest degree. 44 46
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