Question 1

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

Accepted Answer

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° 
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° A

Question 2

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
​

Accepted Answer

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

Question 3

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. ​

Accepted Answer

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

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°​   ​

Accepted Answer

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 
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

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

Accepted Answer

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

Question 6

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
​

Accepted Answer

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° 
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 7

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

Accepted Answer

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

Question 8

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. ​

Accepted Answer

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

Question 9

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. ​

Accepted Answer

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

Question 10

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

Accepted Answer

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 
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 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 = 46°,B = 39°,c = 1.4
​

Accepted Answer

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 
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 12

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.​   ​

Accepted Answer

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

Question 13

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
​

Accepted Answer

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° 
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 14

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
​

Accepted Answer

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° 
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°

Question 15

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?​   ​

Accepted Answer

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

Question 16

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
​

Accepted Answer

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

Question 17

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
​

Accepted Answer

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

Question 18

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
​

Accepted Answer

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

Question 19

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°
​

Accepted Answer

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 
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 20

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

Accepted Answer

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° 
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°

Exam 37:Law of Cosines

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

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 ​

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. ​

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

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

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 ​

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

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 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. ​

Use the law of Cosines to solve the given triangle.Round your answer to two decimal places. ? C = 40°,a = 215\frac { 2 } { 15 }152​ ,b = 15\frac { 1 } { 5 }51​ ?

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 ​

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.​ ​

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 ​

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 ​

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 ​

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 ​

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 ​

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° ​

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

Rectangular Coordinates

Graphs of Equations

Linear Equations in Two Variables

Functions

Analyzing Graphs of Functions

A Library of Parent Functions

Transformations of Functions

Combinations of Functions Composite Functions

Inverse Functions

Mathematical Modeling and Variation

Quadratic Functions and Models

Polynomial Functions of Higher Degree

Polynomial and Synthetic Division

Complex Numbers

Zeros of Polynomial Functions

Rational Functions

Nonlinear Inequalities

Exponential Functions and Their Graphs

Logarithmic Functions and Their Graphs

Properties of Logarithms

Exponential and Logarithmic Equations

Exponential and Logarithmic Models

Radian and Degree Measure

Trigonometric Functions The Unit Circle

Right Triangle Trigonometry

Trigonometric Functions of Any Angle

Graphs of Sine and Cosine Functions

Graphs of Other Trigonometric Functions

Inverse Trigonometric Functions

Applications and Models

Using Fundamental Identities

Verifying Trigonometric Equations

Solving Trigonometric Equations

Sum and Difference Formulas

Multiple Angle and Product to Sum Formulas

Law of Sines

Vectors in the Plane

Vectors and Dot Products

Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

Systems of Inequalities

Linear Programming

Matrices and Systems of Equations

Operations With Matrices

The Inverse of a Square Matrix

The Determinant of a Square Matrix

Applications of Matrices and Determinants

Sequences and Series

Arithmetic Sequences and Partial Sums

Geometric Sequences and Series

Mathematical Induction

The Binomial Theorem

Counting Principles

Probability

Lines

Introduction to Conics Parabolas

Ellipses

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

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

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.

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

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

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 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.

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

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

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.

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

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

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

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

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

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°

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