Question 1

Find the area of the triangle having the indicated angle and sides. ​
B = 71°20',a = 62,c = 24
​
(Round your answer to one decimal place. )
​

Accepted Answer

A) 705.9 
B) ​703.9 
C) ​706.9 
D) ​704.9 
E) ​1,409.7 
A) 705.9 
B) ​703.9 
C) ​706.9 
D) ​704.9 
E) ​1,409.7

Question 2

In the figure,? and ? are positive angles.?   ? a = 3,b = 12
Use ? = arcsin(0.25sin?)to write c as a function of ?.
?

Accepted Answer

A)  $c = \frac { 12 \sin [ \pi - \beta - \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
B)  $c = \frac { 12 \sin [ \pi + \beta - \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
C)  $c = \frac { 0.25 \sin [ \pi - \beta - \arcsin ( 12 \beta ) ] } { \sin \beta }$ 
D)  $c = \frac { 12 \sin [ \pi + \beta + \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
E)  $c = \frac { 12 \sin [ \pi - \beta + \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
A)  $c = \frac { 12 \sin [ \pi - \beta - \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
B)  $c = \frac { 12 \sin [ \pi + \beta - \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
C)  $c = \frac { 0.25 \sin [ \pi - \beta - \arcsin ( 12 \beta ) ] } { \sin \beta }$ 
D)  $c = \frac { 12 \sin [ \pi + \beta + \arcsin ( 0.25 \beta ) ] } { \sin \beta }$ 
E)  $c = \frac { 12 \sin [ \pi - \beta + \arcsin ( 0.25 \beta ) ] } { \sin \beta }$

Question 3

Find values for b such that the triangle has two solutions. ?
A = 32°,a = 5
?

Accepted Answer

A)  $5 \leq b \leq \frac { 5 } { \sin 32 ^ { \circ } }$ 
B)  $5  b > \frac { 5 } { \sin 32 ^ { \circ } }$ 
A)  $5 \leq b \leq \frac { 5 } { \sin 32 ^ { \circ } }$ 
B)  $5  b > \frac { 5 } { \sin 32 ^ { \circ } }$

Question 4

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129°,b = 8,and c = 11

Accepted Answer

A) 34.19 sq.units 
B) 41.03 sq.units 
C) 37.61 sq.units 
D) 30.77 sq.units 
E) 27.36 sq.units 
A) 34.19 sq.units 
B) 41.03 sq.units 
C) 37.61 sq.units 
D) 30.77 sq.units 
E) 27.36 sq.units

Question 5

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​
A = 76°,a = 7,b = 5
​

Accepted Answer

A) B ≈ 43.87°,C ≈ 43.87°,c ≈ 7.96 
B) B ≈ 48.87°,C ≈ 60.13°,c ≈ 6.26 
C) B ≈ 43.87°,C ≈ 60.13°,c ≈ 6.26 
D) B ≈ 48.87°,C ≈ 65.13°,c ≈ 7.96 
E) No Solution 
A) B ≈ 43.87°,C ≈ 43.87°,c ≈ 7.96 
B) B ≈ 48.87°,C ≈ 60.13°,c ≈ 6.26 
C) B ≈ 43.87°,C ≈ 60.13°,c ≈ 6.26 
D) B ≈ 48.87°,C ≈ 65.13°,c ≈ 7.96 
E) No Solution

Question 6

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 ${}^\circ$ ,a = 12.5 and b = 11.5
?

Accepted Answer

A) 68.96 sq.units 
B) 62.06 sq.units 
C) 55.17 sq.units 
D) 82.75 sq.units 
E) 75.85 sq.units 
A) 68.96 sq.units 
B) 62.06 sq.units 
C) 55.17 sq.units 
D) 82.75 sq.units 
E) 75.85 sq.units

Question 7

A straight road makes an angle,A,of 10° with the horizontal.When the angle of elevation,B,of the sun is 56°,a vertical pole beside the road casts a shadow 8 feet long parallel to the road,see figure.Approximate the length of the pole.Round answer to two decimal places.

Accepted Answer

A) 2.48 feet 
B) 10.29 feet 
C) 6.22 feet 
D) 11.86 feet 
E) 6.94 feet 
A) 2.48 feet 
B) 10.29 feet 
C) 6.22 feet 
D) 11.86 feet 
E) 6.94 feet

Question 8

In the figure,? and ? are positive angles.?   ? a = 9,b = 18
Write ? as a function of ?.
?

Accepted Answer

A) ? = arcsin(9sin?) 
B) ? = sin( $\frac { 1 } { 2 }$ sin?) ? 
C) ? = arcsin( $\frac { 1 } { 2 }$ sin?) 
D) ? = sin( $\frac { 1 } { 2 }$ sin?) 
E) ? = arcsin( $\frac { 1 } { 2 }$ sin?) 
A) ? = arcsin(9sin?) 
B) ? = sin( $\frac { 1 } { 2 }$ sin?) ? 
C) ? = arcsin( $\frac { 1 } { 2 }$ sin?) 
D) ? = sin( $\frac { 1 } { 2 }$ sin?) 
E) ? = arcsin( $\frac { 1 } { 2 }$ sin?)

Question 9

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 ${}^\circ$ ,b = 9 and c = 7.

Accepted Answer

A) 29.38 sq.units 
B) 24.48 sq.units 
C) 19.58 sq.units 
D) 22.03 sq.units 
E) 26.93 sq.units 
A) 29.38 sq.units 
B) 24.48 sq.units 
C) 19.58 sq.units 
D) 22.03 sq.units 
E) 26.93 sq.units

Question 10

Find values for b such that the triangle has one solution. ?
A = 44°,a = 6
?

Accepted Answer

A)  $b \leq 6 , b \neq \frac { 6 } { \sin 44 ^ { \circ } }$ 
B)  $b \geq 6 , b \geq \frac { 6 } { \sin 44 ^ { \circ } }$ 
C)  $b \geq 6 , b = \frac { 6 } { \sin 44 ^ { \circ } }$ 
D)  $b > 6 , b > \frac { 6 } { \sin 44 ^ { \circ } }$ 
E)  $b \leq 6 , b = \frac { 6 } { \sin 44 ^ { \circ } }$ 
A)  $b \leq 6 , b \neq \frac { 6 } { \sin 44 ^ { \circ } }$ 
B)  $b \geq 6 , b \geq \frac { 6 } { \sin 44 ^ { \circ } }$ 
C)  $b \geq 6 , b = \frac { 6 } { \sin 44 ^ { \circ } }$ 
D)  $b > 6 , b > \frac { 6 } { \sin 44 ^ { \circ } }$ 
E)  $b \leq 6 , b = \frac { 6 } { \sin 44 ^ { \circ } }$

Question 11

Find values for b such that the triangle has no solutions. ?
A = 64°,a = 340.2
?

Accepted Answer

A)  $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
B)  $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
C)  $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
D)  $b  \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
A)  $b \leq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
B)  $b = \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
C)  $b \geq \frac { 340.2 } { \sin 64 ^ { \circ } }$ 
D)  $b  \frac { 340.2 } { \sin 64 ^ { \circ } }$

Question 12

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 ${}^\circ$ 31 ${}^\prime$ ,a = 10 ?and c = 8.

Accepted Answer

A) 43.33 sq.units 
B) 32.50 sq.units 
C) 28.89 sq.units 
D) 36.11 sq.units 
E) 39.72 sq.units 
A) 43.33 sq.units 
B) 32.50 sq.units 
C) 28.89 sq.units 
D) 36.11 sq.units 
E) 39.72 sq.units

Question 13

Find the area of the triangle having the indicated angle and sides.? $C = 102 ^ { \circ } , a = 6 , b = 2$ ? (Round your answer to one decimal place. )
?

Accepted Answer

A) ?4.9 
B) 5.9 
C) 7.9 
D) 6.9 
E) 11.7 
A) ?4.9 
B) 5.9 
C) 7.9 
D) 6.9 
E) 11.7

Question 14

Find values for b such that the triangle has no solutions. ?
A = 24°,a = 5
?

Accepted Answer

A) $b > \frac { 5 } { \sin 24 ^ { \circ } }$ B) $b \leq \frac { 5 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 5 } { \sin 24 ^ { \circ } }$ D) $b \geq \frac { 5 } { \sin 24 ^ { \circ } }$ E) $b < \frac { 5 } { \sin 24 ^ { \circ } }$ A) $b > \frac { 5 } { \sin 24 ^ { \circ } }$ B) $b \leq \frac { 5 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 5 } { \sin 24 ^ { \circ } }$ D) $b \geq \frac { 5 } { \sin 24 ^ { \circ } }$ E) $b < \frac { 5 } { \sin 24 ^ { \circ } }$

Question 15

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43',a = 6.5,and b = 14

Accepted Answer

A) 30.08 sq.units 
B) 45.11 sq.units 
C) 33.84 sq.units 
D) 41.35 sq.units 
E) 37.59 sq.units 
A) 30.08 sq.units 
B) 45.11 sq.units 
C) 33.84 sq.units 
D) 41.35 sq.units 
E) 37.59 sq.units

Question 16

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 35°,B = 60°,c = 10
​

Accepted Answer

A) C = 85°,a ​≈ 6.76,b ≈ 8.69 
B) C = 85°,a ​≈ 8.69,b ≈ 9.69 
C) C = 85°,a ​≈ 8.76,b ≈ 10.69 
D) C = 85°,a ​≈ 5.76,b ≈ 8.69 
E) ​C = 85°,a ​≈ 7.76,b ≈ 10.69 
A) C = 85°,a ​≈ 6.76,b ≈ 8.69 
B) C = 85°,a ​≈ 8.69,b ≈ 9.69 
C) C = 85°,a ​≈ 8.76,b ≈ 10.69 
D) C = 85°,a ​≈ 5.76,b ≈ 8.69 
E) ​C = 85°,a ​≈ 7.76,b ≈ 10.69

Question 17

Find values for b such that the triangle has two solutions. ?
A = 10°,a = 18.6
?

Accepted Answer

A)  $18.6  b > \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
D)  $18.6 \leq b \leq \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
E)  $18.6 \geq b \geq \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
A)  $18.6  b > \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
D)  $18.6 \leq b \leq \frac { 18.6 } { \sin 10 ^ { \circ } }$ 
E)  $18.6 \geq b \geq \frac { 18.6 } { \sin 10 ^ { \circ } }$

Question 18

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ?
A = 145°,a = 28,b = 8
?

Accepted Answer

A) B ? 0.18°,C ? 32.89° 
B) B ? 0.18°,C ? 39.82° 
C) B ? 9.43°,C ? 25.57° 
D) B ? 25.57°,C ? 9.43° 
E) B ? 39.82°,C ? 0.18° 
A) B ? 0.18°,C ? 32.89° 
B) B ? 0.18°,C ? 39.82° 
C) B ? 9.43°,C ? 25.57° 
D) B ? 25.57°,C ? 9.43° 
E) B ? 39.82°,C ? 0.18°

Question 19

Find the area of the triangle having the indicated angle and sides. ​
С = 84°34',a = 16,b = 26
​
(Round your answer to one decimal place. )
​

Accepted Answer

A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1 
A) 209.1 
B) ​207.1 
C) ​208.1 
D) ​206.1 
E) ​414.1

Question 20

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38',a = 7,and c = 8

Accepted Answer

A) 33.45 sq.units 
B) 27.88 sq.units 
C) 25.09 sq.units 
D) 30.66 sq.units 
E) 22.30 sq.units 
A) 33.45 sq.units 
B) 27.88 sq.units 
C) 25.09 sq.units 
D) 30.66 sq.units 
E) 22.30 sq.units

Exam 36: Law of Sines

Find the area of the triangle having the indicated angle and sides. ​ B = 71°20',a = 62,c = 24 ​ (Round your answer to one decimal place. ) ​

In the figure,? and ? are positive angles.? ? a = 3,b = 12 Use ? = arcsin(0.25sin?)to write c as a function of ?. ?

Find values for b such that the triangle has two solutions. ? A = 32°,a = 5 ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129°,b = 8,and c = 11

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​ A = 76°,a = 7,b = 5 ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 ∘{}^\circ∘ ,a = 12.5 and b = 11.5 ?

A straight road makes an angle,A,of 10° with the horizontal.When the angle of elevation,B,of the sun is 56°,a vertical pole beside the road casts a shadow 8 feet long parallel to the road,see figure.Approximate the length of the pole.Round answer to two decimal places.

In the figure,? and ? are positive angles.? ? a = 9,b = 18 Write ? as a function of ?. ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 ∘{}^\circ∘ ,b = 9 and c = 7.

Find values for b such that the triangle has one solution. ? A = 44°,a = 6 ?

Find values for b such that the triangle has no solutions. ? A = 64°,a = 340.2 ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 ∘{}^\circ∘ 31 ′{}^\prime′ ,a = 10 ?and c = 8.

Find the area of the triangle having the indicated angle and sides.? C=102∘,a=6,b=2C = 102 ^ { \circ } , a = 6 , b = 2C=102∘,a=6,b=2 ? (Round your answer to one decimal place. ) ?

Find values for b such that the triangle has no solutions. ? A = 24°,a = 5 ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 55°43',a = 6.5,and b = 14

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 35°,B = 60°,c = 10 ​

Find values for b such that the triangle has two solutions. ? A = 10°,a = 18.6 ?

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ? A = 145°,a = 28,b = 8 ?

Find the area of the triangle having the indicated angle and sides. ​ С = 84°34',a = 16,b = 26 ​ (Round your answer to one decimal place. ) ​

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 84°38',a = 7,and c = 8

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 Cosines

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Trigonometric Form of a Complex Number

Linear and Nonlinear Systems of Equations

Two Variable Linear Systems

Multivariable Linear Systems

Partial Fractions

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Linear Programming

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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

Find the area of the triangle having the indicated angle and sides. B = 71°20',a = 62,c = 24 (Round your answer to one decimal place. )

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. A = 76°,a = 7,b = 5

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. C = 73 ${}^\circ$ ,a = 12.5 and b = 11.5 ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 129 ${}^\circ$ ,b = 9 and c = 7.

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64 ${}^\circ$ 31 ${}^\prime$ ,a = 10 ?and c = 8.

Find the area of the triangle having the indicated angle and sides.? $C = 102 ^ { \circ } , a = 6 , b = 2$ ? (Round your answer to one decimal place. ) ?

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 35°,B = 60°,c = 10

Find the area of the triangle having the indicated angle and sides. С = 84°34',a = 16,b = 26 (Round your answer to one decimal place. )