Question 1

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​

Accepted Answer

A) b = 16 
B) b = 17 
C) b = 11 
D) b = 15 
E) b = 24 
A) b = 16 
B) b = 17 
C) b = 11 
D) b = 15 
E) b = 24 C

Question 2

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​
A = 130°,a = 40,b = 25
​

Accepted Answer

A) B ≈ 11°,C ≈ 39°,c ≈ 20.05 
B) B ≈ 39°,C ≈ 11°,c ≈ 20.05 
C) B ≈ 28.61°,C ≈ 21.39°,c ≈ 19.05 
D) B ≈ 21.39°,C ≈ 28.61°,c ≈ 19.05 
E) No Solution 
A) B ≈ 11°,C ≈ 39°,c ≈ 20.05 
B) B ≈ 39°,C ≈ 11°,c ≈ 20.05 
C) B ≈ 28.61°,C ≈ 21.39°,c ≈ 19.05 
D) B ≈ 21.39°,C ≈ 28.61°,c ≈ 19.05 
E) No Solution C

Question 3

Find values for b such that the triangle has one solution. ?
A = 74°,a = 17
?

Accepted Answer

A)  $b \geq 17 , b \geq \frac { 17 } { \sin 74 ^ { \circ } }$ 
B)  $b \geq 17 , b = \frac { 17 } { \sin 74 ^ { \circ } }$ 
C)  $b \leq 17 , b \neq \frac { 17 } { \sin 74 ^ { \circ } }$ 
D)  $b \leq 17 , b = \frac { 17 } { \sin 74 ^ { \circ } }$ 
E)  $b > 17 , b > \frac { 17 } { \sin 74 ^ { \circ } }$ 
A)  $b \geq 17 , b \geq \frac { 17 } { \sin 74 ^ { \circ } }$ 
B)  $b \geq 17 , b = \frac { 17 } { \sin 74 ^ { \circ } }$ 
C)  $b \leq 17 , b \neq \frac { 17 } { \sin 74 ^ { \circ } }$ 
D)  $b \leq 17 , b = \frac { 17 } { \sin 74 ^ { \circ } }$ 
E)  $b > 17 , b > \frac { 17 } { \sin 74 ^ { \circ } }$ D

Question 4

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​
A = 120°,a = b = 36
​

Accepted Answer

A) B ≈ 108°,C ≈ 36°,c ≈ 44 
B) B ≈ 36°,C ≈ 108°,c ≈ 23.5 
C) B ≈ 105°,C ≈ 39°,c ≈ 23.5 
D) B ≈ 29°,C ≈ 115°,c ≈ 23.5 
E) No Solution 
A) B ≈ 108°,C ≈ 36°,c ≈ 44 
B) B ≈ 36°,C ≈ 108°,c ≈ 23.5 
C) B ≈ 105°,C ≈ 39°,c ≈ 23.5 
D) B ≈ 29°,C ≈ 115°,c ≈ 23.5 
E) No Solution

Question 5

Find values for b such that the triangle has no solutions. ?
A = 24°,a = 13
?

Accepted Answer

A) ? $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$ B) $b > \frac { 13 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 13 } { \sin 24 ^ { \circ } }$ D) $b < \frac { 13 } { \sin 24 ^ { \circ } }$ E) $b \geq \frac { 13 } { \sin 24 ^ { \circ } }$ A) ? $b \leq \frac { 13 } { \sin 24 ^ { \circ } }$ B) $b > \frac { 13 } { \sin 24 ^ { \circ } }$ C) $b = \frac { 13 } { \sin 24 ^ { \circ } }$ D) $b < \frac { 13 } { \sin 24 ^ { \circ } }$ E) $b \geq \frac { 13 } { \sin 24 ^ { \circ } }$

Question 6

Find values for b such that the triangle has two solutions. ?
A = 46°,a = 10
?

Accepted Answer

A) $10 \geq b \geq \frac { 10 } { \sin 46 ^ { \circ } }$ B) $10 \leq b \leq \frac { 10 } { \sin 46 ^ { \circ } }$ C) $10 > b > \frac { 10 } { \sin 46 ^ { \circ } }$ D) $10 < b \leq \frac { 10 } { \sin 46 ^ { \circ } }$ E) $10 < b < \frac { 10 } { \sin 46 ^ { \circ } }$ A) $10 \geq b \geq \frac { 10 } { \sin 46 ^ { \circ } }$ B) $10 \leq b \leq \frac { 10 } { \sin 46 ^ { \circ } }$ C) $10 > b > \frac { 10 } { \sin 46 ^ { \circ } }$ D) $10 < b \leq \frac { 10 } { \sin 46 ^ { \circ } }$ E) $10 < b < \frac { 10 } { \sin 46 ^ { \circ } }$

Question 7

A straight road makes an angle,A,of 11 ${}^\circ$ with the horizontal.When the angle of elevation,B,of the sun is 52 ${}^\circ$ ,a vertical pole beside the road casts a shadow 6 feet long parallel to the road,see figure.Approximate the length of the pole.Round answer to two decimal places.

Accepted Answer

A) 1.86 feet 
B) 5.63 feet 
C) 6.39 feet 
D) 7.68 feet 
E) 5.00 feet 
A) 1.86 feet 
B) 5.63 feet 
C) 6.39 feet 
D) 7.68 feet 
E) 5.00 feet

Question 8

Select a value for b such that a triangle with A = 33° and a = 4 has no solution.

Accepted Answer

A) 1.84 
B) 3.67 
C) 7.24 
D) 14.68 
E) 1.47 
A) 1.84 
B) 3.67 
C) 7.24 
D) 14.68 
E) 1.47

Question 9

Find values for b such that the triangle has one solution. ?
A = 62°,a = 304.6
?

Accepted Answer

A)  $b \geq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
B)  $b \leq 304.6 , b \neq \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
C)  $b > 304.6 , b > \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
D)  $b \leq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
E)  $b \geq 304.6 , b \geq \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
A)  $b \geq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
B)  $b \leq 304.6 , b \neq \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
C)  $b > 304.6 , b > \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
D)  $b \leq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }$ 
E)  $b \geq 304.6 , b \geq \frac { 304.6 } { \sin 62 ^ { \circ } }$

Question 10

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. ​
C = 64.47°,a = 39,c = 50
​

Accepted Answer

A) A ≈ 70.79°,B ≈ 44.74°,b ≈ 52.32 
B) A ≈ 70.53°,B ≈ 45°,b ≈ 50 
C) A ≈ 44.74°,B ≈ 70.79°,b ≈ 52.32 
D) A ≈ 45°,B ≈ 70.53°,b ≈ 50 
E) No Solution 
A) A ≈ 70.79°,B ≈ 44.74°,b ≈ 52.32 
B) A ≈ 70.53°,B ≈ 45°,b ≈ 50 
C) A ≈ 44.74°,B ≈ 70.79°,b ≈ 52.32 
D) A ≈ 45°,B ≈ 70.53°,b ≈ 50 
E) No Solution

Question 11

Find the area of the triangle having the indicated angle and sides. ​
B = 123°,a = 64,c = 28
​
(Round your answer to one decimal place. )
​

Accepted Answer

A) 750.4 
B) 753.4 
C) 1,502.9 
D) 752.4 
E) 751.4 
A) 750.4 
B) 753.4 
C) 1,502.9 
D) 752.4 
E) 751.4

Question 12

Find values for b such that the triangle has one solution. ?
A = 24?°,a = 16.2
?

Accepted Answer

A)  $b > 16.2 , b > \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
B)  $b \leq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
C)  $b \leq 16.2 , b \neq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
D)  $b \geq 16.2 , b \geq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
E)  $b \geq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
A)  $b > 16.2 , b > \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
B)  $b \leq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
C)  $b \leq 16.2 , b \neq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
D)  $b \geq 16.2 , b \geq \frac { 16.2 } { \sin 24 ^ { \circ } }$ 
E)  $b \geq 16.2 , b = \frac { 16.2 } { \sin 24 ^ { \circ } }$

Question 13

Find the area of the triangle having the indicated angle and sides. ​
A = 10°19',b = 4.6,с = 24
​
(Round your answer to one decimal place. )
​

Accepted Answer

A) 9.9 
B) 8.9 
C) 10.9 
D) 11.9 
E) 19.8 
A) 9.9 
B) 8.9 
C) 10.9 
D) 11.9 
E) 19.8

Question 14

Find values for b such that the triangle has two solutions. ?
A = 66°,a = 307.6
?

Accepted Answer

A) $307.6 b > \frac { 307.6 } { \sin 66 ^ { \circ } }$ D) $307.6 < b < \frac { 307.6 } { \sin 66 ^ { \circ } }$ E) $307.6 \leq b \leq \frac { 307.6 } { \sin 66 ^ { \circ } }$ A) $307.6 b > \frac { 307.6 } { \sin 66 ^ { \circ } }$ D) $307.6 < b < \frac { 307.6 } { \sin 66 ^ { \circ } }$ E) $307.6 \leq b \leq \frac { 307.6 } { \sin 66 ^ { \circ } }$

Question 15

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 ${}^\circ$ ,b = 9 and c = 8.
?

Accepted Answer

A) 38.14 sq.units 
B) 31.79 sq.units 
C) 25.43 sq.units 
D) 28.61 sq.units 
E) 34.96 sq.units 
A) 38.14 sq.units 
B) 31.79 sq.units 
C) 25.43 sq.units 
D) 28.61 sq.units 
E) 34.96 sq.units

Question 16

Because of prevailing winds,a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree,the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree.​   ​c = 43 m B = 96°
​
(Round your answer to two decimal places. )
​

Accepted Answer

A) 24.58 m 
B) 26.58 m 
C) 25.58 m 
D) 28.58 m 
E) 27.58 m 
A) 24.58 m 
B) 26.58 m 
C) 25.58 m 
D) 28.58 m 
E) 27.58 m

Question 17

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​
A = 125°,B = 45°,c = 13
​

Accepted Answer

A) C = 10°,a ≈ 61.33,b ≈ 52.94 
B) C = 10°,a ≈ 54.94,b ≈ 62.33 
C) ​C = 10°,a ≈ 53.94,b ≈ 52.94 
D) ​C = 10°,a ≈ 64.33,b ≈ 52.94 
E) ​C = 10°,a ≈ 63.33,b ≈ 54.94 
A) C = 10°,a ≈ 61.33,b ≈ 52.94 
B) C = 10°,a ≈ 54.94,b ≈ 62.33 
C) ​C = 10°,a ≈ 53.94,b ≈ 52.94 
D) ​C = 10°,a ≈ 64.33,b ≈ 52.94 
E) ​C = 10°,a ≈ 63.33,b ≈ 54.94

Question 18

After a severe storm,three sisters,April,May,and June,stood on their front porch and noticed that the tree in their front yard was leaning 3° from vertical toward the house.From the porch,which is 96 feet away from the base of the tree,they noticed that the angle of elevation to the top of the tree was 31°.Approximate the height of the tree.Round answer to two decimal places. ​

Accepted Answer

A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet 
A) 61.76 feet 
B) 69.64 feet 
C) 56 feet 
D) 59.13 feet 
E) 59.64 feet

Question 19

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​
A = 38°,a = 8,b = 5
​

Accepted Answer

A) B ≈ 29°,C ≈ 113° 
B) B ≈ 22.63°,C ≈ 119.37° 
C) B ≈ 103°,C ≈ 39° 
D) B ≈ 113°,C ≈ 29° 
E) B ≈ 119.37°,C ≈ 22.63° 
A) B ≈ 29°,C ≈ 113° 
B) B ≈ 22.63°,C ≈ 119.37° 
C) B ≈ 103°,C ≈ 39° 
D) B ≈ 113°,C ≈ 29° 
E) B ≈ 119.37°,C ≈ 22.63°

Question 20

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. ​
A = 60°,a = 13,b = 11.6
​

Accepted Answer

A) B ≈ 69.40°,C ≈ 50.6°,c ≈ 11.6 
B) B ≈ 91°,C ≈ 29°,c ≈ 14.05 
C) B ≈ 50.6°,C ≈ 69.40°,c ≈ 14.05 
D) B ≈ 29°,C ≈ 91°,c ≈ 13 
E) No Solution 
A) B ≈ 69.40°,C ≈ 50.6°,c ≈ 11.6 
B) B ≈ 91°,C ≈ 29°,c ≈ 14.05 
C) B ≈ 50.6°,C ≈ 69.40°,c ≈ 14.05 
D) B ≈ 29°,C ≈ 91°,c ≈ 13 
E) No Solution

Exam 36: Law of Sines

Select a value for b such that a triangle with A = 59° and a = 14 has only one solution. ​

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​ A = 130°,a = 40,b = 25 ​

Find values for b such that the triangle has one solution. ? A = 74°,a = 17 ?

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. ​ A = 120°,a = b = 36 ​

Find values for b such that the triangle has no solutions. ? A = 24°,a = 13 ?

Find values for b such that the triangle has two solutions. ? A = 46°,a = 10 ?

A straight road makes an angle,A,of 11 ∘{}^\circ∘ with the horizontal.When the angle of elevation,B,of the sun is 52 ∘{}^\circ∘ ,a vertical pole beside the road casts a shadow 6 feet long parallel to the road,see figure.Approximate the length of the pole.Round answer to two decimal places.

Select a value for b such that a triangle with A = 33° and a = 4 has no solution.

Find values for b such that the triangle has one solution. ? A = 62°,a = 304.6 ?

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. ​ C = 64.47°,a = 39,c = 50 ​

Find the area of the triangle having the indicated angle and sides. ​ B = 123°,a = 64,c = 28 ​ (Round your answer to one decimal place. ) ​

Find values for b such that the triangle has one solution. ? A = 24?°,a = 16.2 ?

Find the area of the triangle having the indicated angle and sides. ​ A = 10°19',b = 4.6,с = 24 ​ (Round your answer to one decimal place. ) ​

Find values for b such that the triangle has two solutions. ? A = 66°,a = 307.6 ?

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 ∘{}^\circ∘ ,b = 9 and c = 8. ?

Because of prevailing winds,a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree,the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree.​ ​c = 43 m B = 96° ​ (Round your answer to two decimal places. ) ​

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. ​ A = 125°,B = 45°,c = 13 ​

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. ​ A = 38°,a = 8,b = 5 ​

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. ​ A = 60°,a = 13,b = 11.6 ​

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Select a value for b such that a triangle with A = 59° and a = 14 has only one solution.

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. A = 130°,a = 40,b = 25

Use the Law of Sines to solve (if possible)the triangle.Round your answers to two decimal places. A = 120°,a = b = 36

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. C = 64.47°,a = 39,c = 50

Find the area of the triangle having the indicated angle and sides. B = 123°,a = 64,c = 28 (Round your answer to one decimal place. )

Find the area of the triangle having the indicated angle and sides. A = 10°19',b = 4.6,с = 24 (Round your answer to one decimal place. )

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. A = 118 ${}^\circ$ ,b = 9 and c = 8. ?

Because of prevailing winds,a tree grew so that it was leaning 6° from the vertical.At a point 43 meters from the tree,the angle of elevation to the top of the tree is 30° (see figure).Find the height a of the tree. c = 43 m B = 96° (Round your answer to two decimal places. )

Use the Law of Sines to solve the triangle.Round your answer to two decimal places. A = 125°,B = 45°,c = 13

Use the Law of Sines to solve for B and C.Round your answer to two decimal places. A = 38°,a = 8,b = 5

Use the Law of Sines to solve (if possible)the triangle.If two solutions exist,find both.Round your answers to two decimal places. A = 60°,a = 13,b = 11.6