Deck 37:Law of Cosines

Question 1

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 170,B = 20°,C = 15°
​

A)Law of Cosines;No solution
B)Law of Sines;A = 145°,b ≈ 76.71,c ≈ 101.37
C)Law of Sines;A = 145°,b ≈ 101.37,c ≈ 76.71
D)Law of Cosines;A = 145°,b ≈ 101.37,c ≈ 76.71
E)Law of Sines;No solution

Answer 1

Law of Sines;A = 145°,b ≈ 101.37,c ≈ 76.71

Question 2

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 20,b = 22,c = 16
​

A)Law of Cosines;No solution
B)Law of Cosines;A ≈ 61.12°,B ≈ 74.41°,C ≈ 44.47°
C)Law of Sines;No solution
D)Law of Sines;A ≈ 61.12°,B ≈ 44.47°,C ≈ 74.41°
E)Law of Sines;A ≈ 61.12°,B ≈ 74.41°,C ≈ 44.47°

Answer 2

Law of Cosines;A ≈ 61.12°,B ≈ 74.41°,C ≈ 44.47°

Question 3

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 50°,b = 4,c = 15
​

A)a ≈ 15,B ≈ 13.85°,C ≈ 116.15°
B)a ≈ 12.80,B ≈ 116.15°,C ≈ 13.85°
C)a ≈ 4,B ≈ 13.85°,C ≈ 116.15°
D)a ≈ 15,B ≈ 15.85°,C ≈ 114.15°
E)a ≈ 12.80,B ≈ 13.85°,C ≈ 116.15°

Answer 3

a ≈ 12.80,B ≈ 13.85°,C ≈ 116.15°

Question 4

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 14,b = 7,C = 118°​ ​

A)A ≈ 42.33°,B ≈ 19.67°,c ≈ 18.36
B)A ≈ 17.67°,B ≈ 17.67°,c ≈ 7
C)A ≈ 44.33°,B ≈ 44.33°,c ≈ 7
D)A ≈ 17.67°,B ≈ 18.36°,c ≈ 18.36
E)A ≈ 44.33°,B ≈ 17.67°,c ≈ 7

Question 5

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 13,b = 17,c = 23
​

A)A ≈ 46.85°,B ≈ 46.85°,C ≈ 86.3°
B)A ≈ 33.91°,B ≈ 99.24°,C ≈ 46.85°
C)A ≈ 46.85°,B ≈ 33.91°,C ≈ 99.24°
D)A ≈ 33.91°,B ≈ 46.85°,C ≈ 99.24°
E)A ≈ 99.24°,B ≈ 46.85°,C ≈ 33.91°

Question 6

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 140°,b = 8,c = 9
​

A)a ≈ 15.98,B ≈ 21.23°,C ≈ 18.77°
B)a ≈ 8,B ≈ 18.77°,C ≈ 21.23°
C)a ≈ 15.98,B ≈ 18.77°,C ≈ 21.23°
D)a ≈ 15.98,B ≈ 20°,C ≈ 20°
E)a ≈ 9,B ≈ 18.77°,C ≈ 21.23°

Question 7

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ​ a = 8,b = 10,c = 14
​

A)A ≈ 101.53°,B ≈ 44.42°,C ≈ 34.05°
B)A ≈ 34.05°,B ≈ 101.53°,C ≈ 44.42°
C)A ≈ 44.42°,B ≈ 44.42°,C ≈ 91.16°
D)A ≈ 44.42°,B ≈ 34.05°,C ≈ 101.53°
E)A ≈ 34.05°,B ≈ 44.42°,C ≈ 101.53°

Question 8

Use the Heron's formula to find the area of the triangle.Round your answer to two decimal places. ​
A = 10,b = 14,c = 19
​

A)14.68
B)84.31
C)54.99
D)31.75
E)68.09

Question 9

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. A = 29°,b = 14,c = 29 ​

A)a ≈ 18.08,B ≈ 22.05°,C ≈ 128.95°
B)a ≈ 29,B ≈ 24.05°,C ≈ 126.95°
C)a ≈ 18.08,B ≈ 128.95°,C ≈ 22.05°
D)a ≈ 14,B ≈ 22.05°,C ≈ 128.95°
E)a ≈ 29,B ≈ 22.05°,C ≈ 128.95°

Question 10

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​
A = 33,b = 36,c = 25
​

A)58.21
B)353.71
C)450.18
D)564.33
E)399.04

Question 11

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 23°,a = 3,b = 17
​

A)Law of Sines;No solution
B)Law of Cosines;No solution
C)Law of Cosines;c ≈ 3,B ≈ 43°,C ≈ 114°
D)Law of Cosines;c ≈ 6,B ≈ 43°,C ≈ 114°
E)Law of Sines;c ≈ 17,B ≈ 114°,C ≈ 43°

Question 12

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 75.4,b = 52,c = 52
​
​

A)A ≈ 43.53°,B ≈ 92.94°,C ≈ 43.53°
B)A ≈ 43.53°,B ≈ 97.94°,C ≈ 38.53°
C)A ≈ 43.53°,B ≈ 38.53°,C ≈ 97.94°
D)A ≈ 92.94°,B ≈ 43.53°,C ≈ 43.53°
E)A ≈ 97.94°,B ≈ 38.53°,C ≈ 43.53°

Question 13

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​
A = 18,b = 20,C = 65°
​

A)Law of Sines;A ≈ 65°,B ≈ 52.79°,c ≈ 20
B)Law of Sines;A ≈ 52.79°,B ≈ 65°,c ≈ 20
C)Law of Cosines;A ≈ 52.79°,B ≈ 62.21°,c ≈ 20.49
D)Law of Sines;No solution
E)Law of Cosines;No solution

Question 14

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places.​ a = 9,b = 5,c = 10

A)A ≈ 29.93°,B ≈ 63.90°,C ≈ 86.18°
B)A ≈ 86.18°,B ≈ 29.93°,C ≈ 63.90°
C)A ≈ 86.18°,B ≈ 63.90°,C ≈ 29.93°
D)A ≈ 63.90°,B ≈ 86.18°,C ≈ 29.93°
E)A ≈ 63.90°,B ≈ 29.93°,C ≈ 86.18°

Question 15

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ?
C = 40°,a = $\frac { 2 } { 15 }$ ,b = $\frac { 1 } { 5 }$ ?

A)A ? 41.21°,B ? 98.79°,c ? 0.13
B)A ? 99.76°,B ? 98.76°,c ? 0.13
C)A ? 98.76°,B ? 41.24°,c ? 0.20
D)A ? 41.24°,B ? 98.76°,c ? 0.20
E)A ? 98.79°,B ? 41.21°,c ? 0.20

Question 16

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 1.62,b = 0.95,c = 1.45
​

A)A ≈ 35.51°,B ≈ 82.06°,C ≈ 62.43°
B)A ≈ 62.43°,B ≈ 35.51°,C ≈ 82.06°
C)A ≈ 82.06°,B ≈ 35.51°,C ≈ 62.43°
D)A ≈ 82.06°,B ≈ 62.43°,C ≈ 35.51°
E)A ≈ 62.43°,B ≈ 82.06°,C ≈ 35.51°

Question 17

Determine whether the Law of Sines or the Law of Cosines is needed to solve the triangle.Then solve the triangle.Round your answer to two decimal places. ​
A = 46°,B = 39°,c = 1.4
​

A)Law of Cosines;No solution
B)Law of Sines;No solution
C)Law of Cosines;C = 95°,a ≈ 0.88,b ≈ 1.01
D)Law of Sines;C = 95°,a ≈ 1.01,b ≈ 0.88
E)Law of Sines;C = 95°,a ≈ 1.01,b ≈ 1.01

Question 18

Use the low of Cosines to solve the given triangle.Round your answer to two decimal places. ​
A = 51,b = 21,c = 68
​

A)A ≈ 30.37°,B ≈ 12.02°,C ≈ 137.61°
B)A ≈ 30.37°,B ≈ 137.61°,C ≈ 12.02°
C)A ≈ 12.02°,B ≈ 30.37°,C ≈ 137.61°
D)A ≈ 137.61°,B ≈ 12.02°,C ≈ 30.37°
E)A ≈ 137.61°,B ≈ 30.37°,C ≈ 12.02°

Question 19

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​
A = 3.2,b = 10.9,c = 9
​

A)7.0
B)6.4
C)3.7
D)45.3
E)12.6

Question 20

Determine whether the Law of Sines or the Law of Cosine is needed to solve the triangle.Then solve the triangle. ​
A = 9,c = 6,B = 50°
​

A)Law of Sines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
B)Law of Cosines;A ≈ 88.21°,C ≈ 41.79°,b ≈ 6.9
C)Law of Cosines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
D)Law of Sines;A ≈ 41.79°,C ≈ 88.21°,b ≈ 6.9
E)Law of Sines;No solution

Question 21

Given a = 10,b = 12,and c = 8,use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. ​

A)82.82°
B)55.77°
C)41.41°
D)80.44°
E)60.33°

Question 22

Given a = 7,b = 10,and c = 11,use the Law of Cosines to solve the triangle for the value of С.Round your answer to two decimal places. Figure not drawn to scale

A)62.96°
B)80.44°
C)78.46°
D)38.57°
E)60.33°

Question 23

On a map,Orlando is 187 millimeters due south of Niagara Falls,Denver is 282 millimeters from Orlando,and Denver is 244 millimeters from Niagara Falls (see figure).Find the bearing of Denver from Niagara Falls. ​​ ​

A)S 77.6° W
B)S 78.6° W
C)S 80.6° W
D)S 82.6° W
E)S 83.6° W

Question 24

Use the Heron's formula to find the area of the triangle.Round your answer upto one decimal place. ​
A = 3.08,b = 0.78,c = 2.48
​

A)3.5
B)0.1
C)0.4
D)0.40
E)0.7

Question 25

You want to buy a triangular lot measuring 1360 feet by 1870 feet by 2500 feet.The price of the land is $2200 per acre.How much does the land cost? (Hint: 1 acre = 43,560 square feet)
​

A)$63,450.91
B)$63,300.91
C)$63,400.91
D)$63,200.91
E)$63,320.91

Question 26

Given a = 12,b = 14,and c = 7,use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. ​

A)80.44°
B)91.02°
C)58.98°
D)29.99°
E)60.33°

Question 27

To determine the distance between two aircraft,a tracking station continuously determines the distance to each aircraft and the angle A between them (see figure).Determine the distance a between the planes when A = 44°,b = 37 miles,and c = 22 miles.​ ​

A)35.60 miles
B)31.81 miles
C)26.11 miles
D)11.27 miles
E)54.99 miles

Question 28

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ?
A = $\frac { 1 } { 2 }$ ,b = $\frac { 2 } { 3 }$ ,c = $\frac { 1 } { 3 }$ ?

A)0.08
B)0.10
C)0.12
D)0.06
E)0.11

Question 29

Given a = 10,b = 14,and c = 9,use the Law of Cosines to solve the triangle for the value of B.Round your answer to two decimal places. Figure not drawn to scale

A)94.78°
B)80.44°
C)39.84°
D)45.38°
E)60.33°

Question 30

To determine the distance between two aircraft,a tracking station continuously determines the distance to each aircraft and the angle between them (see figure).Determine the distance a between the planes when A = 52° miles,b = 22 miles,and c = 19 miles.​ ​

A)18.2 mi
B)20.2 mi
C)36.9 mi
D)24.2 mi
E)21.2 mi

Question 31

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ?
A = 1,b = $\frac { 1 } { 3 }$ ,c = $\frac { 3 } { 4 }$ ?

A)0.65
B)0.09
C)2.29
D)0.66
E)0.50

Question 32

Determine the angle ? in the design of the streetlight shown in the following figure.Round your answer upto decimal place.? $$a = 6 , b = 7 \frac { 1 } { 2 } , c = 5$$ ? ? ?

A)80.5°
B)95.5°
C)75.5°
D)85.5°
E)90.5°

Question 33

Given a = 9,b = 13,and c = 8,use the Law of Cosines to solve the triangle for the value of A.Round your answer to two decimal places. Figure not drawn to scale

A)99.59°
B)80.44°
C)37.36°
D)43.05°
E)60.33°

Question 34

Given a = 8,b = 14,and c = 12,use the Law of Cosines to solve the triangle for the value of C.Round your answer to two decimal places. ​

A)60.33°
B)86.42°
C)58.81°
D)34.77°
E)80.44°

Question 35

You want to buy a triangular lot measuring 500 yards by 830 yards by 1110 yards.The price of the land is $2000 per acre.How much does the land cost? (Hint: 1 acre = 4840 square yards)
​

A)$80,335.71
B)$80,465.71
C)$80,415.71
D)$80,315.71
E)$80,215.71

Question 36

The lengths of the sides of a triangular parcel of land are approximately 400 feet,700 feet,and 800 feet.Approximate the area of the parcel. ​

A)180,710.4 ft²
B)139,977.7 ft²
C)94,372.9 ft²
D)207,620.4 ft²
E)108,426.2 ft²

Question 37

To approximate the length of a marsh,a surveyor walks 255 meters from point A to point B,then turns 81° and walks 225 meters to point C (see figure).Approximate the length AC of the marsh.​ ​ where a = 225 m,b = 255 m
​

A)365.5 m
B)359.5 m
C)370.5 m
D)371.5 m
E)360.5 m

Question 38

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ​
A = 78.2,b = 52,c = 52
​

A)771.91
B)​140.43
C)​80.66
D)​769.91
E)1340.39

Question 39

The baseball player in center field is playing approximately 310 feet from the television camera that is behind home plate.A batter hits a fly ball that goes to the wall 400 feet from the camera (see figure).The camera turns 10° to follow the play.Approximately how far does the center fielder have to run to make the catch?​ ​

A)102.9 ft
B)114.9 ft
C)108.9 ft
D)113.9 ft
E)103.9 ft

Question 40

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal place. ​
A = 13.22,b = 9.36,c = 15.95
​

A)35.77
B)​14.09
C)​79.16
D)​61.84
E)​48.31

Question 41

Given a = 11,b = 14,and c = 10,use Heron's Area Formula to find the area of triangle ABC.Round your answer to two decimal places. ​

A)54.64
B)47.04
C)41.31
D)48.87
E)43.32

Question 42

Given a = 4.6,b = 6.1,and c = 9.1,use Heron's Area Formula to find the area of ΔABC.Round your answer to two decimal places. ​

A)10.79
B)9.89
C)12.60
D)8.58
E)12.09

Question 43

A vertical pole 29 feet tall stands on a hillside that makes an angle of 20° with the horizontal.Determine the approximate length of cable that would be needed to reach from the top of the pole to a point 65 feet downhill from the base of the pole.Round your answer to two decimal places. ​

A)70.59 feet
B)61.45 feet
C)84.70 feet
D)75.29 feet
E)79.72 feet