College Trigonometry, 2011a

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916 Applications of <strong>Trigonometry</strong> 11.3.1 Exercises In Exercises 1 - 10, use the Law of Cosines to find the remaining side(s) and angle(s) if possible. 1. a =7,b=12,γ=59.3 ◦ 2. α = 104 ◦ ,b=25,c=37 3. a = 153, β=8.2 ◦ ,c= 153 4. a =3,b=4,γ=90 ◦ 5. α = 120 ◦ ,b=3,c=4 6. a =7,b=10,c=13 7. a =1,b=2,c=5 8. a = 300, b= 302, c=48 9. a =5,b=5,c= 5 10. a =5,b=12, ; c =13 In Exercises 11 - 16, solve for the remaining side(s) and angle(s), if possible, using any appropriate technique. 11. a =18,α=63 ◦ ,b= 20 12. a =37,b=45,c=26 13. a =16,α=63 ◦ ,b= 20 14. a =22,α=63 ◦ ,b=20 15. α =42 ◦ ,b= 117, c= 88 16. β =7 ◦ ,γ= 170 ◦ ,c=98.6 17. Find the area of the triangles given in Exercises 6, 8 and 10 above. 18. The hour hand on my antique Seth Thomas schoolhouse clock in 4 inches long and the minute hand is 5.5 inches long. Find the distance between the ends of the hands when the clock reads four o’clock. Round your answer to the nearest hundredth of an inch. 19. A geologist wants to measure the diameter of a crater. From her camp, it is 4 miles to the northern-most point of the crater and 2 miles to the southern-most point. If the angle between the two lines of sight is 117 ◦ , what is the diameter of the crater? Round your answer to the nearest hundredth of a mile. 20. From the Pedimaxus International Airport a tour helicopter can fly to Cliffs of Insanity Point by following a bearing of N8.2 ◦ E for 192 miles and it can fly to Bigfoot Falls by following a bearing of S68.5 ◦ E for 207 miles. 6 Find the distance between Cliffs of Insanity Point and Bigfoot Falls. Round your answer to the nearest mile. 21. Cliffs of Insanity Point and Bigfoot Falls from Exericse 20 above both lie on a straight stretch of the Great Sasquatch Canyon. What bearing would the tour helicopter need to follow to go directly from Bigfoot Falls to Cliffs of Insanity Point? Round your angle to the nearest tenth of a degree. 6 Please refer to Page 905 in Section 11.2 for an introduction to bearings.
11.3 The Law of Cosines 917 22. A naturalist sets off on a hike from a lodge on a bearing of S80 ◦ W. After 1.5 miles, she changes her bearing to S17 ◦ W and continues hiking for 3 miles. Find her distance from the lodge at this point. Round your answer to the nearest hundredth of a mile. What bearing should she follow to return to the lodge? Round your angle to the nearest degree. 23. The HMS Sasquatch leaves port on a bearing of N23 ◦ E and travels for 5 miles. It then changes course and follows a heading of S41 ◦ E for 2 miles. How far is it from port? Round your answer to the nearest hundredth of a mile. What is its bearing to port? Round your angle to the nearest degree. 24. The SS Bigfoot leaves a harbor bound for Nessie Island which is 300 miles away at a bearing of N32 ◦ E. A storm moves in and after 100 miles, the captain of the Bigfoot finds he has drifted off course. If his bearing to the harbor is now S70 ◦ W, how far is the SS Bigfoot from Nessie Island? Round your answer to the nearest hundredth of a mile. What course should the captain set to head to the island? Round your angle to the nearest tenth of a degree. 25. From a point 300 feet above level ground in a firetower, a ranger spots two fires in the Yeti National Forest. The angle of depression 7 made by the line of sight from the ranger to the first fire is 2.5 ◦ and the angle of depression made by line of sight from the ranger to the second fire is 1.3 ◦ . The angle formed by the two lines of sight is 117 ◦ . Find the distance between the two fires. Round your answer to the nearest foot. (Hint: In order to use the 117 ◦ angle between the lines of sight, you will first need to use right angle <strong>Trigonometry</strong> to find the lengths of the lines of sight. This will give you a Side-Angle-Side case in which to apply the Law of Cosines.) fire 117 ◦ fire firetower 26. If you apply the Law of Cosines to the ambiguous Angle-Side-Side (ASS) case, the result is a quadratic equation whose variable is that of the missing side. If the equation has no positive real zeros then the information given does not yield a triangle. If the equation has only one positive real zero then exactly one triangle is formed and if the equation has two distinct positive real zeros then two distinct triangles are formed. Apply the Law of Cosines to Exercises 11, 13 and 14 above in order to demonstrate this result. 27. Discuss with your classmates why Heron’s Formula yields an area in square units even though four lengths are being multiplied together. 7 See Exercise 78 in Section 10.3 for the definition of this angle.
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College Trigonometry Version ⌊π
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Table of Contents vii 10 Foundation
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Preface Thank you for your interest
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xi text and we have gone to great l
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Chapter 10 Foundations of Trigonome
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10.1 Angles and their Measure 695 k
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10.1 Angles and their Measure 697 2
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10.1 Angles and their Measure 701 T
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10.1 Angles and their Measure 703 y
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10.1 Angles and their Measure 707 h
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10.1 Angles and their Measure 711 I
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10.2 The Unit Circle: Cosine and Si
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10.3 The Six Circular Functions and
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10.5 Graphs of the Trigonometric Fu
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10.7 Trigonometric Equations and In
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11.5 Graphs of Polar Equations 967
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11.7 Polar Form of Complex Numbers
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11.8 Vectors 1013 Q ′ (1, 7) up 4
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11.8 Vectors 1019 The remaining pro
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11.8 Vectors 1027 11.8.1 Exercises
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Index n th root of a complex number
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Index 1071 central angle, 701 chang
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College Trigonometry, 2011a

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