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Math 175: Cloutier Exam 5 Name: _____________________________________ SP2013 ID: __________________________ Instructions: Spread out! Cover your tests! Keep your eyes on your own papers! You may use your calculators, but NO CELL PHONES! Remove all ear pieces. Put away all electronic devices, the time will be written on the board. Show your work on EVERY problem. Points will not be awarded without sufficient work. You will be given FIFTY-FIVE MINUTES for this Exam. The following formulas may be needed: Page # 2 3 4 Total 22 38 40 100 Points Earned Possible 1 Math 175: Cloutier Exam 5 SP2013 1. (10pts) The angle of inclination from the base of skyscraper A to the top of skyscraper B is 10.8 . If skyscraper B is 1414 feet tall, how far apart are the two skyscrapers? 1414 ft 10.8* tan 10.80 opp adj 1414 tan 10.80 x 1414 x 7, 412.45 ft tan 10.80 2. (12pts) Find the value of the angle . Left : sin 2 4 & Right : sin h2 h8 2 4 h 2 h8 Since both have sin , put them together! Obviously, solve for h: 2h 16 4h 8 8 2h h 4 Now solve for theta: Use the Left , doubled : sin 2 2 2 1 2 sin 1 38.9o 6 3 Math 175: Cloutier Exam 5 SP2013 3. (18pts) An aircraft is spotted in the sky between two observers who are 1900 feet apart on flat land. The first person measures the angle of elevation to the airplane to be 35 and the second person measures the angle of elevation to the airplane to be 30 . How high is the airplane? b 30* 35* 1900 ft There’s 180* in a triangle: 180 – 35 – 30 = 115* sin 115o 1900 sin 30o b b 1900sin 30o sin 115o 1048.2 ft Now use right triangle trigonometry: 1900sin 30o sin 35o h o o sin 35 h b sin 35 34, 449.26 ft b sin 115o 4. (20pts) Solve the triangle: b 4 , c 5 , B 40 sin 40o 4 5sin 40 sin C sin C 5 4 o remember that sine is positive in Q1 and Q2: 5sin 40o 53.5o Q1 answer: C sin 4 5sin 40o 126.5o Q2 answer: 180 sin 4 Thus: A 180 40 53.5 86.5o Thus: A 180 40 126.5 13.5o 1 sin 86.50 a sin 400 4 a 4sin 86.50 sin 400 1 6.2 3 sin 13.50 a sin 400 4 a 4sin 13.50 sin 400 1.5 Math 175: Cloutier Exam 5 SP2013 5. A ship travels 12 miles per hour. Its original destination was 600 miles away. To avoid a storm, the ship traveled 7 hours off course, at an angle of 31 . a. (20pts) Solve the shown triangle: 12miles / hr v v s s 12 s 84miles t 7 b2 6002 842 2 600 84 cos 310 b 529.8miles sin 31 sin C C 4.68o 529.8 84 And hence A 180 4.68 31 144.32o b. (5pts) Find the area of the triangle you solved above. 1 1 A ab sin C 600 529.8 sin 4.68o 12,968mi 2 2 2 6. (15pts) Find the area of the following triangle: a 7 , b 5 , c 8 82 7 2 52 2 7 5 cos C 64 49 25 70 1 1 64 49 25 Area ab cos C 7 5 2.5 2 2 70 cos C cos sin sin cos 1 tan 1 cot cos sin cos sin cos 2 sin 2 cos2 sin 2 1 tan 1 cot 1 sin 1 cos cos sin sin cos cos sin cos sin cos sin 2 2 cos sin cos sin cos sin cos sin cos sin cos sin Bonus: Establish the identity: 4