Question 1

Determine the angle  θ	hetaθ  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

Accepted Answer

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

Question 2

Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] 
 -u

Accepted Answer

A)   
B)    
C)    
D)    
E)  none of these

Question 3

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

Accepted Answer

A)    b≥304.6,b=304.6sin⁡62∘b \geq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }b≥304.6,b=sin62∘304.6​ 
B)    b≤304.6,b≠304.6sin⁡62∘b \leq 304.6 , b 
eq \frac { 304.6 } { \sin 62 ^ { \circ } }b≤304.6,b=sin62∘304.6​ 
C)     304.6 , b > \frac { 304.6 } { \sin 62 ^ { \circ } }">b>304.6,b>304.6sin⁡62∘b > 304.6 , b > \frac { 304.6 } { \sin 62 ^ { \circ } }b>304.6,b>sin62∘304.6​ 
D)    b≤304.6,b=304.6sin⁡62∘b \leq 304.6 , b = \frac { 304.6 } { \sin 62 ^ { \circ } }b≤304.6,b=sin62∘304.6​ 
E)    b≥304.6,b≥304.6sin⁡62∘b \geq 304.6 , b \geq \frac { 304.6 } { \sin 62 ^ { \circ } }b≥304.6,b≥sin62∘304.6​

Question 4

Write the complex number in trigonometric form.

Accepted Answer

A)    Z=3(cos⁡π−icos⁡π) Z = 3 ( \cos \pi - i \cos \pi ) Z=3(cosπ−icosπ)  
B)     Z=3(cos⁡π+isin⁡π) Z = 3 ( \cos \pi + i \sin \pi ) Z=3(cosπ+isinπ)  
C)    Z=−3(cos⁡π+isin⁡π) Z = - 3 ( \cos \pi + i \sin \pi ) Z=−3(cosπ+isinπ)  
D)     Z=3(cos⁡π2−isin⁡π2) Z = 3 \left( \cos \frac { \pi } { 2 } - i \sin \frac { \pi } { 2 } \right) Z=3(cos2π​−isin2π​)  
E)     Z=3(cos⁡3π2+isin⁡3π2) Z = 3 \left( \cos \frac { 3 \pi } { 2 } + i \sin \frac { 3 \pi } { 2 } \right) Z=3(cos23π​+isin23π​)

Question 5

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​
Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.
​

Accepted Answer

A)  18.1 lb
B)  21.1 lb
C)  19.1 lb
D)  20.1 lb
E)  17.1 lb

Question 6

Given  u=⟨−5,−6⟩\mathbf { u } = \langle - 5 , - 6 \rangleu=⟨−5,−6⟩  and  v=⟨−6,−5⟩\mathbf { v } = \langle - 6 , - 5 \ranglev=⟨−6,−5⟩  , find  u.vu^. v u.v  .

Accepted Answer

A)  0
B)  30
C)  60
D)  61
E)  -11

Question 7

Use the vectors  u=⟨2,2⟩\mathbf { u } = \langle 2,2 \rangleu=⟨2,2⟩  ,  v=⟨−2,2⟩\mathbf { v } = \langle - 2,2 \ranglev=⟨−2,2⟩  to find the indicated quantity.State whether the result is a vector or a scalar.    3u⋅v3 \mathbf { u } \cdot \mathbf { v }3u⋅v

Accepted Answer

A)    ⟨0,2⟩\langle 0,2 \rangle⟨0,2⟩  ; vector
B)  -2; scalar
C)  2; scalar
D)    ⟨4,−4⟩\langle 4 , - 4 \rangle⟨4,−4⟩  ; vector
E)  0; scalar

Question 8

Determine the area of a triangle having the following measurements.Round your answer to two decimal places. B = 64  ∘^\circ∘  31  ′&#x27;′  , 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

Question 9

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

Question 10

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

Question 11

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

Question 12

Find a unit vector in the direction of the given vector.  
   u=⟨4,0⟩\mathbf { u } = \langle 4,0 \rangleu=⟨4,0⟩

Accepted Answer

A)    ⟨1,1⟩\langle 1,1 \rangle⟨1,1⟩ 
B)    ⟨1,0⟩\langle 1,0 \rangle⟨1,0⟩ 
C)    ⟨0,0⟩\langle 0,0 \rangle⟨0,0⟩ 
D)    ⟨4,0⟩\langle 4,0 \rangle⟨4,0⟩ 
E)    ⟨0,1⟩\langle 0,1 \rangle⟨0,1⟩

Question 13

Represent the following complex number graphically.  
   3(cos⁡160∘+isin⁡160∘) 3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right) 3(cos160∘+isin160∘)

Accepted Answer

A)   
B)   
C)    
D)   
E)

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 = 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

Question 15

Find the angle  θ	hetaθ   between the vectors.    u=⟨6,2⟩v=⟨7,0⟩\begin{array} { l } \mathbf { u } = \langle 6,2 angle \\mathbf { v } = \langle 7,0 angle\end{array}u=⟨6,2⟩v=⟨7,0⟩​   
(Round the answer to 2 decimal places.)

Accepted Answer

A)    18.43∘18.43 ^ { \circ }18.43∘ 
B)    33.43∘33.43 ^ { \circ }33.43∘ 
C)    23.43∘23.43 ^ { \circ }23.43∘ 
D)    28.43∘28.43 ^ { \circ }28.43∘ 
E)    38.43∘38.43 ^ { \circ }38.43∘

Question 16

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

Question 17

Determine whether u are v and orthogonal, parallel, or neither.  u=⟨−43,32⟩,v=⟨16,−18⟩\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangleu=⟨3−4​,23​⟩,v=⟨16,−18⟩

Accepted Answer

A)  neither
B)  parallel
C)  orthogonal

Question 18

Use the vectors  u=⟨3,6⟩\mathbf { u } = \langle 3,6 \rangleu=⟨3,6⟩  ,  v=⟨−6,5⟩\mathbf { v } = \langle - 6,5 \ranglev=⟨−6,5⟩  to find the indicated quantity.State whether the result is a vector or a scalar.    (u⋅v) v( \mathbf { u } \cdot \mathbf { v } )  \mathbf { v }(u⋅v) v

Accepted Answer

A)    ⟨−72,60⟩\langle - 72,60 \rangle⟨−72,60⟩  ; vector
B)    ⟨−72,64⟩\langle - 72,64 \rangle⟨−72,64⟩  ; vector
C)  -72; scalar
D)  60; scalar
E)    ⟨−72,58⟩\langle - 72,58 \rangle⟨−72,58⟩  ; vector

Question 19

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. ​
A = 60°, a = 36, c = 40
​

Accepted Answer

A)  C ≈ 105.79°, B ≈ 45.79°or​C ≈ 74.21°, B ≈ 14.21°
B)  ​C ≈ 74.21°, B ≈ 45.79°or​C ≈ 105.79°, B ≈ 14.21°
C)  ​C ≈ 10°, B ≈ 110°or​C ≈ 25.5°, B ≈ 104.5°
D)  ​C ≈ 45.79°, B ≈ 74.21°or​C ≈ 14.21°, B ≈ 105.79°
E)  ​C ≈ 60°, B ≈ 60°or​C ≈ 45°, B ≈ 75°

Question 20

Find the vector v that has a magnitude of 9 and is in the same direction as u, where  u=⟨6,−5⟩\mathbf { u } = \langle 6 , - 5 \rangleu=⟨6,−5⟩  .

Accepted Answer

A)     v=⟨56161,−66161⟩\mathbf { v } = \left\langle \frac { 5 \sqrt { 61 } } { 61 } , - \frac { 6 \sqrt { 61 } } { 61 } \right\ranglev=⟨61561c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,−61661c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​⟩ 
B)     v=⟨456161,−546161⟩\mathrm { v } = \left\langle \frac { 45 \sqrt { 61 } } { 61 } , - \frac { 54 \sqrt { 61 } } { 61 } \right\ranglev=⟨614561c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,−615461c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​⟩ 
C)     v=⟨6161,−6161⟩\mathbf { v } = \left\langle \frac { \sqrt { 61 } } { 61 } , - \frac { \sqrt { 61 } } { 61 } \right\ranglev=⟨6161c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,−6161c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​⟩ 
D)     v=⟨66161,−56161⟩\mathbf { v } = \left\langle \frac { 6 \sqrt { 61 } } { 61 } , - \frac { 5 \sqrt { 61 } } { 61 } \right\ranglev=⟨61661c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,−61561c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​⟩ 
E)     v=⟨546161,−456161⟩\mathbf { v } = \left\langle \frac { 54 \sqrt { 61 } } { 61 } , - \frac { 45 \sqrt { 61 } } { 61 } \right\ranglev=⟨615461c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​,−614561c-2.7,0,-7.17,-2.7,-13.5,-8c-5.8,-5.3,-9.5,-10,-9.5,-14c0,-2,0.3,-3.3,1,-4c1.3,-2.7,23.83,-20.7,67.5,-54c44.2,-33.3,65.8,-50.3,66.5,-51c1.3,-1.3,3,-2,5,-2c4.7,0,8.7,3.3,12,10s173,378,173,378c0.7,0,35.3,-71,104,-213c68.7,-142,137.5,-285,206.5,-429c69,-144,104.5,-217.7,106.5,-221l0 -0c5.3,-9.3,12,-14,20,-14H400000v40H845.2724s-225.272,467,-225.272,467s-235,486,-235,486c-2.7,4.7,-9,7,-19,7c-6,0,-10,-1,-12,-3s-194,-422,-194,-422s-65,47,-65,47zM834 80h400000v40h-400000z'/>​​⟩

Exam 6: Additional Topics In Trigonometery

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.

Correct Answer
verified

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

Correct Answer
verified

Use the Law of Sines to solve for C and B.Round your answer to two decimal places. A = 60°, a = 36, c = 40

Correct Answer
verified

Correct Answer
verified

Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle 4,0 \rangle$

Correct Answer
verified

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.)

Correct Answer
verified

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

Correct Answer
verified

Find the angle $\theta$ between the vectors. $\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\\mathbf { v } = \langle 7,0 \rangle\end{array}$ (Round the answer to 2 decimal places.)

Correct Answer
verified

Use the vectors $\mathbf { u } = \langle 2,2 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $3 \mathbf { u } \cdot \mathbf { v }$

Correct Answer
verified

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

Correct Answer
verified

Represent the following complex number graphically. $3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right)$ $Represent the following complex number graphically. 3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right) A) B) C) D) E)$

Correct Answer
verified

A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.

Correct Answer
verified

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

Correct Answer
verified

Given $\mathbf { u } = \langle - 5 , - 6 \rangle$ and $\mathbf { v } = \langle - 6 , - 5 \rangle$ , find $u^. v$ .

Correct Answer
verified

Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] -u

Correct Answer
verified

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

Correct Answer
verified

Find the vector v that has a magnitude of 9 and is in the same direction as u, where $\mathbf { u } = \langle 6 , - 5 \rangle$ .

Correct Answer
verified

Use the vectors $\mathbf { u } = \langle 3,6 \rangle$ , $\mathbf { v } = \langle - 6,5 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }$

Correct Answer
verified

Correct Answer
verified

Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangle$

Correct Answer
verified

Exam 6: Additional Topics In Trigonometery

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. ​ ​

Correct AnswerverifiedShow Answer

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

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Use the Law of Sines to solve for C and B.Round your answer to two decimal places. ​ A = 60°, a = 36, c = 40 ​

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Write the complex number in trigonometric form.

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Find a unit vector in the direction of the given vector. u=⟨4,0⟩\mathbf { u } = \langle 4,0 \rangleu=⟨4,0⟩

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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.)

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

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Find the angle θ\thetaθ between the vectors. u=⟨6,2⟩v=⟨7,0⟩\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\\mathbf { v } = \langle 7,0 \rangle\end{array}u=⟨6,2⟩v=⟨7,0⟩​ (Round the answer to 2 decimal places.)

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Use the vectors u=⟨2,2⟩\mathbf { u } = \langle 2,2 \rangleu=⟨2,2⟩ , v=⟨−2,2⟩\mathbf { v } = \langle - 2,2 \ranglev=⟨−2,2⟩ to find the indicated quantity.State whether the result is a vector or a scalar. 3u⋅v3 \mathbf { u } \cdot \mathbf { v }3u⋅v

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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 ​

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Represent the following complex number graphically. 3(cos⁡160∘+isin⁡160∘) 3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right) 3(cos160∘+isin160∘)

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A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. ​ Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place. ​

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

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Given u=⟨−5,−6⟩\mathbf { u } = \langle - 5 , - 6 \rangleu=⟨−5,−6⟩ and v=⟨−6,−5⟩\mathbf { v } = \langle - 6 , - 5 \ranglev=⟨−6,−5⟩ , find u.vu^. v u.v .

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Using the figure below, sketch a graph of the given vector.[The graphs in the answer choices are drawn to the same scale as the graph below.] -u

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

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Find the vector v that has a magnitude of 9 and is in the same direction as u, where u=⟨6,−5⟩\mathbf { u } = \langle 6 , - 5 \rangleu=⟨6,−5⟩ .

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Use the vectors u=⟨3,6⟩\mathbf { u } = \langle 3,6 \rangleu=⟨3,6⟩ , v=⟨−6,5⟩\mathbf { v } = \langle - 6,5 \ranglev=⟨−6,5⟩ to find the indicated quantity.State whether the result is a vector or a scalar. (u⋅v) v( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }(u⋅v) v

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Determine the angle θ\thetaθ 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

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Determine whether u are v and orthogonal, parallel, or neither. u=⟨−43,32⟩,v=⟨16,−18⟩\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangleu=⟨3−4​,23​⟩,v=⟨16,−18⟩

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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.

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Use the Law of Sines to solve for C and B.Round your answer to two decimal places. A = 60°, a = 36, c = 40

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Find a unit vector in the direction of the given vector. $\mathbf { u } = \langle 4,0 \rangle$

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

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Find the angle $\theta$ between the vectors. $\begin{array} { l } \mathbf { u } = \langle 6,2 \rangle \\\mathbf { v } = \langle 7,0 \rangle\end{array}$ (Round the answer to 2 decimal places.)

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Use the vectors $\mathbf { u } = \langle 2,2 \rangle$ , $\mathbf { v } = \langle - 2,2 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $3 \mathbf { u } \cdot \mathbf { v }$

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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

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Represent the following complex number graphically. $3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right)$ $Represent the following complex number graphically. 3 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right) A) B) C) D) E)$

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A force of F pounds is required to pull an object weighing W pounds up a ramp inclined at θ degrees from the horizontal. Find F if W = 100 pounds and θ = 11°.Approximate the answer to one decimal place.

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

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Given $\mathbf { u } = \langle - 5 , - 6 \rangle$ and $\mathbf { v } = \langle - 6 , - 5 \rangle$ , find $u^. v$ .

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

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Find the vector v that has a magnitude of 9 and is in the same direction as u, where $\mathbf { u } = \langle 6 , - 5 \rangle$ .

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Use the vectors $\mathbf { u } = \langle 3,6 \rangle$ , $\mathbf { v } = \langle - 6,5 \rangle$ to find the indicated quantity.State whether the result is a vector or a scalar. $( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }$

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Determine whether u are v and orthogonal, parallel, or neither. $\mathbf { u } = \left\langle \frac { - 4 } { 3 } , \frac { 3 } { 2 } \right\rangle , \mathbf { v } = \langle 16 , - 18 \rangle$

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