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lessons 9.7 and 9.8.notebook April 29, 2016 Lessons 9.7 and 9.8: Trigonometric Ratios Objective: students will use trigonometric ratios to find unknown lengths of right triangles. Apr 288:49 PM 1 lessons 9.7 and 9.8.notebook April 29, 2016 Key Vocabulary trigonometric ratios: a ratio of the lengths of two sides of a right triangle. tangent (acute angle of right triangle): the ratio of the length of the side opposite the angle to the side adjacent to the angle sine (acute angle of right triangle): the ratio of the length of the side opposite the angle to the length of the hypothenuse cosine (acute angles of a right triangle): the ratio of the length of the side adjacent to the length of the hypothenuse Apr 288:52 PM 2 lessons 9.7 and 9.8.notebook April 29, 2016 Apr 289:20 PM 3 lessons 9.7 and 9.8.notebook April 29, 2016 Example 1: Finding the Tangent Ratio For ABC. find the tangent of angle B B 36 C hypothenuse 85 77 A Apr 289:00 PM 4 lessons 9.7 and 9.8.notebook April 29, 2016 Checkpoint B 36 C For ABC. find the tangent of angle A hypothenuse 85 77 A Apr 289:05 PM 5 lessons 9.7 and 9.8.notebook April 29, 2016 Example 2: Using Calculators to Find the Tangent a. tan 18 b. tan 45 Apr 289:08 PM 6 lessons 9.7 and 9.8.notebook April 29, 2016 Checkpoint tan 35 tan 10 Apr 289:12 PM 7 lessons 9.7 and 9.8.notebook April 29, 2016 Example 3: Using Tangent Ratio When the sun's rays strike the moon's surface at an angle of 6 , the edge of a lunar crater casts a shadow that has a length of about 4700 meters. What is the depth of the crater? Apr 289:11 PM 8 lessons 9.7 and 9.8.notebook April 29, 2016 Example 4: Finding the Sine and Cosine Ratio Find the sine and cosine of angle L. J 8 K 17 15 L Apr 289:15 PM 9 lessons 9.7 and 9.8.notebook April 29, 2016 Checkpoint J 8 K Find the sine and cosine of angle J 17 15 L Apr 289:21 PM 10 lessons 9.7 and 9.8.notebook April 29, 2016 Example 5: Using a Calculator to Find Sine and Cosine a. sin 38 b. cos 43 Apr 289:22 PM 11 lessons 9.7 and 9.8.notebook April 29, 2016 Checkpoint Approximate sin 74 and cos 12 Apr 289:26 PM 12 lessons 9.7 and 9.8.notebook April 29, 2016 Example 6: Using Cosine Ratio F Use the Cosine Ratio to find the unknown length 16 41 E x D Apr 289:27 PM 13 lessons 9.7 and 9.8.notebook April 29, 2016 Example 7: Using a Sine Ratio Use the sine ratio to find the unknown length. 164 x 27 Apr 289:34 PM 14