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Law of SinesMultiple ChoiceIdentify the choice that best completes the statement or answers the question.____1.Use the Law of Sines to solve for all possible triangles that satisfy a = 45, c = 24, ?A = 123? conditions.a.?B = 30?, ?C = 27?, b= 33c.?B = 32?, ?C = 26?, b= 26b.?B = 30?, ?C = 27?, b= 27d.?B = 27?, ?C = 30?, b= 314521200132080____2.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____3.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?____4.Find the indicated side x if b = 6, a = 33?, y = 70?. a.22.369b.14.527c.3.354d.5.164____5.Find the indicated angle ? if a = 120, c = 135, ? = 33?. a.95?b.85?c.81?d.93?4749800144145____6.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 ft4483100-101600____7.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 ft366395091440____8.A pilot is flying over a straight highway. He determines the angles of depression to two mileposts, c = 6 mi apart, to be ?m = 28?, ?k = 51?.(a) Find the distance of the plane from point A.(b) Find the elevation of the plane.a.The distance of the plane from point A = 4.8, the elevation of the plane = 2.2b.The distance of the plane from point A = 5.9, the elevation of the plane = 2.2c.The distance of the plane from point A = 4.8, the elevation of the plane = 4.4d.The distance of the plane from point A = 2.2, the elevation of the plane = 2.4469900082550____9.A communication tower is located at the top of a steep hill, as shown. The angle of inclination of the hill is m = 55o. A guy wire is to be attached to the top of the tower and to the ground, 102 m downhill from the base of the tower. The angle k in the figure is determined to be 11o. Find the length of cable required for the guy wire.a.The length of cable required for the guy wire is 149 mb.The length of cable required for the guy wire is 144 mc.The length of cable required for the guy wire is 134 md.The length of cable required for the guy wire is 138 mNumeric Response10.Use the Law of Sines to find the indicated angle ?. Please round the answer to the nearest tenth.190500? = __________ ?11.Use the Law of Sines to find the indicated side x. Please round the answer to the nearest tenth.19049-2540x ? __________12.For the triangle shown, find the length AD. Please round the answer to the nearest hundredth. AD = __________13.Points A and B are separated by a lake. To find the distance between them, a surveyor locates a point C on land such that ?CAB = 48.8?. He also measures CA as 318 ft and CB as 523 ft. Find the distance between A and B. Please round the answer to the nearest tenth. __________ ft14.A short-wave radio antenna is supported by two guy wires, 155 ft and 175 ft long. Each wire is attached to the top of the antenna and anchored to the ground, at two anchor points on opposite sides of the antenna. The shorter wire makes an angle of 63? with the ground. How far apart are the anchor points? Please round the answer to the nearest tenth.__________ ft4603750-9525015.A tree on a hillside casts a shadow 219 ft down the hill. If the angle of inclination of the hillside is 23? to the horizontal and the angle of elevation of the sun is 54?, find the height of the tree. Please round the answer to the nearest integer. __________ ft475615011874516.A water tower 40 m tall is located at the top of a hill. From a distance of 120 m down the hill, it is observed that the angle formed between the top and base of the tower is 5?. Find the angle of inclination of the hill. Please round the answer to the nearest tenth.__________ ?17.Find the area of the shaded figure, correct to two decimals. A = __________18.Find the area of the shaded figure, correct to two decimals. A = __________NAME: _______________________________________________ CSY: ________________ DATE: ______________MAKE-UP ITEMS FOR MIDTERM PERIODANSWER SHEETMULTIPLE CHOICE_______________________________________________________________NUMERIC RESPONSE _________________________________________________________________________________________________________________________________________________________________________________________________________________________________ ................
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