Question 1

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. ​

Accepted Answer

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 
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 2

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. ​

Accepted Answer

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

Question 3

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
​

Accepted Answer

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

Question 4

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

Accepted Answer

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° 
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 5

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)
​

Accepted Answer

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

Question 6

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
​

Accepted Answer

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

Question 7

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

Accepted Answer

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° 
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 8

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

Accepted Answer

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° 
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 9

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 = $\frac { 1 } { 3 }$ ?

Accepted Answer

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

Question 10

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

Accepted Answer

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° 
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 11

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. ​

Accepted Answer

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

Question 12

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

Accepted Answer

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

Question 13

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
​

Accepted Answer

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

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 = 170,B = 20°,C = 15°
​

Accepted Answer

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 
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

Question 15

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)
​

Accepted Answer

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

Question 16

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 = $\frac { 3 } { 4 }$ ?

Accepted Answer

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

Question 17

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°
​

Accepted Answer

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 
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 18

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

Accepted Answer

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° 
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°

Question 19

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.​   ​

Accepted Answer

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

Question 20

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. ​​   ​

Accepted Answer

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 
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

Exam 37:Law of Cosines

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. ​

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. ​

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 ​

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

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) ​

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 ​

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

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

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ? A = 12\frac { 1 } { 2 }21​ ,b = 23\frac { 2 } { 3 }32​ ,c = 13\frac { 1 } { 3 }31​ ?

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

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. ​

Determine the angle ? in the design of the streetlight shown in the following figure.Round your answer upto decimal place.? a=6,b=712,c=5a = 6 , b = 7 \frac { 1 } { 2 } , c = 5a=6,b=721​,c=5 ? ? ?

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 ​

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° ​

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) ​

Use the Heron's formula to find the area of the triangle.Round your answer upto two decimal places. ? A = 1,b = 13\frac { 1 } { 3 }31​ ,c = 34\frac { 3 } { 4 }43​ ?

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° ​

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

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.​ ​

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. ​​ ​

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

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Trigonometric Form of a Complex Number

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Multivariable Linear Systems

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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

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.

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.

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

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

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)

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

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

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

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 = $\frac { 1 } { 3 }$ ?

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

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.

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

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°

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)

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 = $\frac { 3 } { 4 }$ ?

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°

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

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.

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.