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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 find x. Let a = 85, ?A = 34.6?. a.132b.135c.133d.134____2.Use the Law of Sines to find x. Let c = 21, ?A = 58?. a.23b.25c.24d.46____3.Use the Law of Sines to find angle C. Let a = 28, and c = 13. a.23ob.30oc.25od.24o____4.Solve the triangle using the Law of Sines. Let ?A = 54?, ?B = 16?. a.?C = 109?, b = 20, a = 59c.?C = 120?, b = 19, a = 57b.?C = 110?, b = 19, a = 56d.?C = 112?, b = 17, a = 56____5.Use the Law of Sines to solve for all possible triangles that satisfy a = 23, b = 14, ?A =113? conditions.a.?B = 33?, ?C = 38?, c= 15c.?B = 38?, ?C = 42?, c= 16b.?B = 35?, ?C = 32?, c= 17d.?B = 34?, ?C = 33?, c= 14____6.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= 31____7.Use the Law of Sines to solve for all possible triangles that satisfy b = 23, c = 35, ?B = 25? conditions.a.?A = 115?, ?C = 40?, a = 49c.?A = 114?, ?C = 42?, a = 47b.?A = 117?, ?C = 40?, a = 55d.?A = 119?, ?C = 39?, a = 51____8.Use the Law of Sines to solve for all possible triangles that satisfy a = 92, b = 54, ?A = 45? conditions.a.?B = 29?, ?C = 108?, c = 117c.?B = 25?, ?C = 111?, c = 120b.?B = 26?, ?C = 110?, c = 124d.?B = 25?, ?C = 110?, c = 1224406900-6350____9.The path of a satellite orbiting the earth causes it to pass directly over two tracking stations A and B, which are 51 mi apart. When the satellite is on one side of the two stations, the angles of elevation at A and B are measured to be ?m = 85.5?, ?k =79.8?.(a) How far is the satellite from station A?(b) How high is the satellite above the ground?a.The distance of the satellite from station A = 511.4, the satellite is high above the ground as 493.8.b.The distance of the satellite from station A = 473.4, the satellite is high above the ground as 481.8.c.The distance of the satellite from station A = 505.4, the satellite is high above the ground as 503.8.d.The distance of the satellite from station A = 525.4, the satellite is high above the ground as 514.8.3727450142875____10.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 = 2.43759200120015____11.To find the distance across a river, a surveyor chooses points A and B, which are 197 ft apart on one side of the river (see the figure). She then chooses a reference point (C) on the opposite side of the river and finds that ?A = 47? and ?B = 70?. Approximate the distance from A to C.a.206 ftb.209 ftc.208 ftd.207 ft4254500147955____12.A tree on a hillside casts a shadow b = 209 ft down the hill. If the angle of inclination of the hillside is 22o to the horizontal and the angle of elevation of the sun is 54o, find the height of the tree. a.The height of the tree is 184 ftc.The height of the tree is 190 ftb.The height of the tree is 188 ftd.The height of the tree is 186 ft469900082550____13.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 Response14.Use the Law of Sines to find the indicated angle ?. Please round the answer to the nearest tenth.190500? = __________ ?15.Use the Law of Sines to find the indicated side x. Please round the answer to the nearest tenth.19049-2540x ? __________16.For the triangle shown, find the length AD. Please round the answer to the nearest hundredth. AD = __________17.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. __________ ft18.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.__________ ft4603750-9525019.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. __________ ft475615011874520.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.__________ ? ................
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