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Law of CosinesMultiple Choice396875095250Identify the choice that best completes the statement or answers the question.____1.Use the Law of Cosines to determine side x if b = 9, c = 18, and ? = 27?. a.55.32b.10.78c.26.34d.116.314356100123190____2.Use the Law of Cosines to determine angle ? if a = 69.19, b = 35.97, c = 42.82.a.15.79?b.63.29?c.44.21?d.25.97?4521200132080____3.Use the Law of Cosines to determine side x if a = 30, c = 36 and ? = 25? correct to two decimal places.a.26.98b.7.42c.15.44d.13.12____4.Solve triangle ABC, if a = 17, b = 10, and ?C = 117?. a.c = 28.31, ?A = 43.53?, ?B = 22.47?c.c = 23.31, ?A = 40.53?, ?B = 22.47?b.c = 23.31, ?A = 40.53?, ?B = 19.47?d.c = 23.31, ?A = 35.02?, ?B = 27.98?____5.Solve triangle ABC if a = 12, b = 18, c = 14.a.?A = 88.271?, ?B = 49.977?, ?C = 41.752?b.?A = 40.752?, ?B = 51.977?, ?C = 87.271?c.?A = 41.752?, ?B = 87.271?, ?C = 50.977?d.?A = 87.271?, ?B = 41.752?, ?C = 49.977?____6.Solve triangle ABC, if a = 71, ?B = 56?, ?C = 67.?a.b = 70.2, c = 77.9, ?A = 57?c.b = 72.2, c = 75.9, ?A = 59?b.b = 74.2, c = 73.9, ?A = 62?d.b = 73.2, c = 73.9, ?A = 57?____7.Find the indicated side x if b = 6, a = 33?, y = 70?. a.22.369b.14.527c.3.354d.5.164____8.Find the indicated angle ? if a = 120, c = 135, ? = 33?. a.95?b.85?c.81?d.93?____9.Two straight roads diverge at an angle of 30 degrees. Two cars leave the intersection at 5:00 P.M., one traveling at 45 mi/h, and the other at 35 mi/h. How far apart are the cars at 5:30 P.M.a.9.7 milesb.13.7 milesc.10.9 milesd.11.4 miles____10.A car travels along a straight road, heading east for 2 h, then traveling for 50 min on another road that leads north-east. If the car has maintained the constant speed of 60, how far (in miles) is it from its starting position?a.127.46 milesb.175.26 milesc.143.39 milesd.159.33 miles387350081915____11.Two tugboats that are 118 ft apart pull a barge, as shown. If the length of one cable is 206 and the length of the other is 227, find the angle formed by the two cables.a.37.38?b.28.03?c.31.15?d.43.61?417195043180____12.A boy is flying two kites at the same time. He has 450 ft of line out to one kite and 390 ft to the other. He estimates the angle between the two lines to be 34o. Approximate the distance between the kites.a.252.21 ftb.302.65 ftc.353.09 ftd.327.87 ft4749800144145____13.A 50 foot tower is located on the side of a mountain that is inclined 35? to the horizontal. A guy wire is to be attached to the top of the tower and anchored at a point 145 feet downhill from the base of the tower. Find the shortest length of wire needed.a.178.44 ftb.107.92 ftc.249.82 ftd.214.13 ft4508500116840____14.The CN Tower in Toronto, Canada, is the tallest free-standing structure in the world. A woman on the observation deck, 1,100 ft above the ground, wants to determine the distance between two landmarks on the ground below. She observes that the angle ?? formed by the lines of sight to these two landmarks is 50. She also observes that the angle between the vertical and the line of sight of one of the landmarks a, is 47 and to the other landmark ?? is 45. Find the distance between the two landmarks. a.1,340 ftb.2,872 ftc.2,067 ftd.2,241 ftNumeric Response15.Find the area of the triangle whose sides have the given lengths. a = 4, b = 13, c = 15. A = __________16.Find the area of the shaded figure, correct to two decimals. A = __________17.Find the area of the shaded figure, correct to two decimals. A = __________18.Land in downtown Columbia is valued at $10 a square foot. What is the value of a triangular lot with sides of lengths 119, 147, and 190 ft? Please round the answer to the nearest dollar.law of cosinesAnswer SectionMULTIPLE CHOICE1.ANS:BPTS:12.ANS:DPTS:13.ANS:CPTS:14.ANS:CPTS:15.ANS:CPTS:16.ANS:APTS:17.ANS:CPTS:18.ANS:BPTS:19.ANS:DPTS:110.ANS:DPTS:111.ANS:CPTS:112.ANS:APTS:113.ANS:APTS:114.ANS:APTS:1NUMERIC RESPONSE17.ANS:24PTS:118.ANS:7.64PTS:119.ANS:7.65PTS:125.ANS:$87,461PTS:1 ................
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