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FeatureLesson Geometry Lesson Main For each triangle, find (a) the length of the leg opposite B and (b) the length of the leg adjacent to B. (For help,

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Presentation on theme: "FeatureLesson Geometry Lesson Main For each triangle, find (a) the length of the leg opposite B and (b) the length of the leg adjacent to B. (For help,"— Presentation transcript:

1 FeatureLesson Geometry Lesson Main For each triangle, find (a) the length of the leg opposite B and (b) the length of the leg adjacent to B. (For help, go to Lesson 8-3.) Lesson 8-4 Sine and Cosine Ratios 1.3.2. Check Skills Youll Need 8-4

2 FeatureLesson Geometry Lesson Main 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: 2 78. 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: 3 29. Solutions Lesson 8-4 Sine and Cosine Ratios Check Skills Youll Need 8-4

3 FeatureLesson Geometry Lesson Main 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. Find x to the nearest whole number. 4.5. 28 15 8 15 52 29 Lesson 8-3 The Tangent Ratio Lesson Quiz 8-4

4 FeatureLesson Geometry Lesson Main Textbook

5 FeatureLesson Geometry Lesson Main Textbook

6 FeatureLesson Geometry Lesson Main Lesson 8-4 Sine and Cosine Ratios Notes 8-4 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.

7 FeatureLesson Geometry Lesson Main Use the triangle to find sin T, cos T, sin G, and cos G. Write your answer in simplest terms. Lesson 8-4 Sine and Cosine Ratios sin T = = 12 20 3535 = opposite hypotenuse cos T = = 16 20 4545 = adjacent hypotenuse sin G = = 16 20 4545 = opposite hypotenuse cos G = = 12 20 3535 = adjacent hypotenuse Quick Check Additional Examples 8-4 Writing Sine and Cosine Ratios

8 FeatureLesson Geometry Lesson Main 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. Lesson 8-4 Sine and Cosine Ratios cos 35° = height 20 Use the cosine ratio. height = 20 cos 35°Solve for height. 20 35 16.383041 Use a calculator. The flagpole is about 16 ft tall. Quick Check Additional Examples 8-4 Real-World Connection

9 FeatureLesson Geometry Lesson Main 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. 0.375 67.975687 Round to the nearest degree.m A 68 Lesson 8-4 Sine and Cosine Ratios Additional Examples 8-4 Using the Inverse of Sine and Cosine

10 FeatureLesson Geometry Lesson Main (continued) To find m B, use the fact that the acute angles of a right triangle are complementary. The acute angles, rounded to the nearest degree, measure 68 and 22. m A + m B = 90Definition of complementary angles Substitute.68 + m B 90 m B 22 Lesson 8-4 Sine and Cosine Ratios Quick Check Additional Examples 8-4

11 FeatureLesson Geometry Lesson Main 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. 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 Lesson 8-4 Sine and Cosine Ratios Use this figure for Exercises 5 and 6. 5.Find x to the nearest degree. 6.Find y to the nearest degree. 44 46 sin A = or, sin B = or 16 34 30 34 8 17 15 17 cos A = or, cos B = or 16 34 30 34 15 17 8 17 Lesson Quiz 8-4


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