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GEOMETRY MODULE 2 LESSON 28 SOLVING PROBLEMS USING SINE AND COSINE OPENING EXERCISE Complete the table below without looking at previous notes. π½ π° ππ° ππ° ππ° ππ° Sine 0 1 2 β2 2 β3 2 1 Cosine 1 β3 2 β2 2 1 2 0 WORKBOOK ο· Complete Exercise 1a with a partner. You may use the information below to help you. Let x represent the distance from school to Jannethβs house. Since sin 41 = 5.3 , then 8 300 π₯ = 5.3 8 . π₯ = 452.8301887 β¦ For the rest of the lecture, you will need a calculator with trigonometric functions. Be sure you are in degree mode. Together we will use calculators to find the value of sin 10°. ο· Complete the table in Exercise 2. Round all results to the ten-thousandth place. ο· What do you notice about the numbers in the row sin π compared with the numbers in the row cos π? The numbers are the same but reversed in order. Letβs find the values of a and b. Round final results to two decimal places. MOD2 L28 1 We can find the length of side a using sin 40 and cos 50. π sin 40 = 26 26 sin 40 = π 26(0.6428) β π π β 16.71 We can find the length of side b using sin 50 and cos 40. sin 50 = π 26 26 sin 50 = π 26(0.7660) β π π β 19.92 ο· Complete Exercise 5. A shipmate set a boat to sail exactly 27° NE from the dock. After traveling 120 miles, the shipmate realized he had misunderstood the instruction from the captain; he was supposed to set sail going directly east! a. How many miles will the shipmate have to travel directly south before he is directly east of the dock? Round your answer to the nearest mile. Let S represent the distance they travel directly south. sin 27 = π 120 π = 120 sin 27 = 54.47885997 β¦ He traveled approximately 54 miles south. b. How many extra miles does the shipmate travel by going the wrong direction compared to going directly east? Round your answer to the nearest mile. Let E represent the distance they travel directly south. cos 27 = πΈ 120 πΈ = 120 cos 27 = 106.927829 β¦ He traveled approximately 107 miles east The total distance traveled by the boat is 120 + 54 = 174. They ended up 107 miles east of the dock. So they traveled 174 β 107 = 67 extra miles. MOD2 L28 2 DISCUSSION Johanna borrowed some tools from a friend so that she could precisely, but not exactly, measure the corner space in her backyard to plant some vegetables. She wants to build a fence to prevent her dog from digging up the seeds that she plants. Johanna returned the tools to her friend before making the most important measurement: the one that would give the length of the fence! Johanna decided that she could just use the Pythagorean theorem to find the length of the fence she would need. Is the Pythagorean theorem applicable in this situation? Explain. No. The corner of her backyard is not a 90° anlge. What can we do to help Johanna figure out the length of fence she needs? Consider the following. The missing side is equal to π₯ + π¦. π₯ cos 35 = 100 π₯ = 100 cos 35 cos 50 = π¦ 74.875 π¦ = 74.875 cos 50 π₯ + π¦ = 100 cos 35 + 74.875 cos 50 β 81.92 + 48.12872 β 130.05 ON YOUR OWN Complete Exercise 6 in your workbook. π₯ + π¦ = 4.04 cos 39 + 3.85 cos 42 β 3.139669 + 2.861107 β 6.000776 MOD2 L28 3 SUMMARY Solving Right Triangles ο· If two sides are known, then the Pythagorean theorem can be used to determine the length of the third side. ο· If one side is known and the measure of one of the acute angles is known, the sine, cosine, or tangent can be used. ο· If the triangle is known to be similar to another triangle where the side lengths are given, then corresponding ratios or knowledge of the scale factor can be used to determine the unknown length. ο· Direct measurement can be used. Solving Other Triangles ο· You can find the length of an unknown side length of a triangle when you know two of the side lengths and the missing side is between two acute angles. Split the triangle into two right triangles, and find the lengths of two pieces of the missing side. HOMEWORK Problem Set Module 2 Lesson 28, page 217 #1, 2a and b, 3, 4, 6: Show all work in an organized and linear manner. Μ Μ can make NOTE: For Problem 4, there are two correct answers to this problem since the segment Μ Μ πΆπ an angle of 48° above or below the horizon in four distinct locations, providing two different heights above the ground. Choose the angle below the horizon. DUE: Tuesday, Jan 17, 2017 MOD2 L28 4