Question 1

Draw a sketch to represent the vector. Refer to the vectors pictured here. 
-a + (c + d)

Accepted Answer

A) 
 
B)

Question 2

Solve the problem.
-If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 4,6 \rangle$, and $\mathbf { w } = \langle - 11,2 \rangle$, evaluate $\mathbf { u } \cdot ( \mathbf { v } - \mathbf { w } )$.

Accepted Answer

A)  $- 3$ 
B)  $- 7$ 
C)  $- 12$ 
D)  20

Question 3

Solve the problem.
-A solar reflector is made using 29 identical triangular-shaped mirrors, each having sides 1.7 meters, 1.9 meters, 1.1 meters. What is the total surface area of the reflector (to the nearest square
Meter)?

Accepted Answer

A)  $30 \mathrm {~m} ^ { 2 }$ 
B)  $27 \mathrm {~m} ^ { 2 }$ 
C)  $31 \mathrm {~m} ^ { 2 }$ 
D)  $25 \mathrm {~m} ^ { 2 }$

Question 4

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate.
-$$\begin{array} { l } 
a = 6.3 \mathrm { in } . \
b = 13.6 \mathrm { in } . \
c = 15.3 \mathrm { in } .
\end{array}$$

Accepted Answer

A)  No triangle satisfies the given conditions. 
B)  $\mathrm { A } = 24.3 ^ { \circ } , \mathrm { B } = 62.6 ^ { \circ } , \mathrm { C } = 93.1 ^ { \circ }$ 
C)  $\mathrm { A } = 26.3 ^ { \circ } , \mathrm { B } = 60.6 ^ { \circ } , \mathrm { C } = 93.1 ^ { \circ }$ 
D)  $\mathrm { A } = 22.3 ^ { \circ } , \mathrm { B } = 62.6 ^ { \circ } , \mathrm { C } = 95.1 ^ { \circ }$

Question 5

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides,
by the law of sines.
-b, B, and c

Accepted Answer

A) Yes 
B) No

Question 6

Write the vector in the form ai + bj.
--5, 6

Accepted Answer

A) 5i + 6j 
B) 6i + 5j 
C) -5i + 6j 
D) 6i - 5j

Question 7

Solve the problem.
-A painter needs to cover a triangular region 61 meters by 69 meters by 72 meters. A can of paint covers 70 square meters. How many cans will be needed?

Accepted Answer

A) 14 cans 
B) 318 cans 
C) 3 cans 
D) 28 cans

Question 8

Find the dot product for the pair of vectors.
--13, 10 , 0, 9

Accepted Answer

A) -117 
B) 90 
C) 77 
D) 103

Question 9

Determine whether the pair of vectors is orthogonal.
-$$\langle - 8 , - 1 \rangle , \langle - 8,32 \rangle$$

Accepted Answer

A)  Yes 
B)  No

Question 10

Sketch the vectors u and w with angle between them and sketch the resultant.
-$$| \mathbf { u } | = 8 , | \mathbf { w } | = 3 , \theta = 80 ^ { \circ }$$

Accepted Answer

A) 
 
B)

Question 11

Find the indicated vector.
-Let $\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }$. Find $6 \mathbf { u } + \mathbf { v }$.

Accepted Answer

A)  $19 i + 6 j$ 
B)  $\mathbf { i } + 19 \mathrm { j }$ 
C)  $19 i + j$ 
D)  $11 \mathrm { i } + \mathrm { j }$

Question 12

Find the missing parts of the triangle.
-B = 44°20' b = 12.30
A = 31.26
If necessary, round side lengths to the nearest hundredth.

Accepted Answer

A) A = 43°10', C = 94°30', c = 45.06 
B) A = 40°10', C = 95°30', c = 40.56 
C) no such triangle 
D) A = 42°10', C = 93°30', c = 43.56

Question 13

Determine the number of triangles ABC possible with the given parts.
-$$a = 32 , b = 65 , A = 79 ^ { \circ }$$

Accepted Answer

A)  3 
B)  1 
C)  0 
D)  2

Question 14

Find the missing parts of the triangle.
-$$\begin{array} { l } 
\mathrm { B } = 104.3 ^ { \circ } \
\mathrm { a } = 298 \mathrm {~cm} \
\mathrm {~b} = 1324 \mathrm {~cm}
\end{array}$$
If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$.

Accepted Answer

A)  $\mathrm { A } = 12.6 ^ { \circ } , \mathrm { C } = 63.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$ 
B)  no such triangle 
C)  $\mathrm { A } = 15.6 ^ { \circ } , \mathrm { C } = 60.1 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$ 
D)  $\mathrm { A } = 63.1 ^ { \circ } , \mathrm { C } = 12.6 ^ { \circ } , \mathrm { c } = 1218 \mathrm {~cm}$

Question 15

Find the missing parts of the triangle.
-
If necessary, round angles to the nearest degree and give exact values of side lengths.

Accepted Answer

A)  no such triangle 
B)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 6 \sqrt { 3 } + 6$ 
C)  $\mathrm { A } = 75 ^ { \circ } , \mathrm { C } = 45 ^ { \circ } , \mathrm { c } = 6 \sqrt { 3 } + 6$ 
D)  $\mathrm { A } = 45 ^ { \circ } , \mathrm { C } = 75 ^ { \circ } , \mathrm { c } = 6 \sqrt { 3 }$

Question 16

Draw a sketch to represent the vector. Refer to the vectors pictured here. 
-$$\frac { 1 } { 2 } a$$

Accepted Answer

A) 
 
B)

Question 17

Solve the problem.
-Two ships leave a harbor together traveling on courses that have an angle of 129° between them. If they each travel 505 miles, how far apart are they (to the nearest mile)?

Accepted Answer

A) 41 mi 
B) 1824 mi 
C) 912 mi 
D) 435 mi

Question 18

Find the indicated vector.
-Let $\mathbf { u } = \langle 6 , - 8 \rangle$. Find $9 \mathbf { u }$.

Accepted Answer

A)  $\langle - 54 , - 72 \rangle$ 
B)  $\langle - 54,72 \rangle$ 
C)  $\langle 54 , - 72 \rangle$ 
D)  $\langle 54,72 \rangle$

Question 19

Determine the number of triangles ABC possible with the given parts.
-b = 42, c = 52, B = 106°

Accepted Answer

A) 0 
B) 1 
C) 3 
D) 2

Question 20

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary.
-a = 13.6 cm b = 18.4 cm
C = 15.3 cm

Accepted Answer

A)  $108 \mathrm {~cm} ^ { 2 }$ 
B)  $102 \mathrm {~cm} ^ { 2 }$ 
C)  $105 \mathrm {~cm} ^ { 2 }$ 
D)  $111 \mathrm {~cm} ^ { 2 }$

Exam 7: Applications of Trigonometry and Vectors

Draw a sketch to represent the vector. Refer to the vectors pictured here. -a + (c + d)

Solve the problem. -If $\mathbf { u } = \langle - 5,7 \rangle , \mathbf { v } = \langle - 4,6 \rangle$ , and $\mathbf { w } = \langle - 11,2 \rangle$ , evaluate $\mathbf { u } \cdot ( \mathbf { v } - \mathbf { w } )$ .

Solve the problem. -A solar reflector is made using 29 identical triangular-shaped mirrors, each having sides 1.7 meters, 1.9 meters, 1.1 meters. What is the total surface area of the reflector (to the nearest square Meter) ?

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - $\begin{array} { l } a = 6.3 \mathrm { in } . \\b = 13.6 \mathrm { in } . \\c = 15.3 \mathrm { in } .\end{array}$

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -b, B, and c

Write the vector in the form ai + bj. --5, 6

Solve the problem. -A painter needs to cover a triangular region 61 meters by 69 meters by 72 meters. A can of paint covers 70 square meters. How many cans will be needed?

Find the dot product for the pair of vectors. --13, 10 , 0, 9

Determine whether the pair of vectors is orthogonal. - $\langle - 8 , - 1 \rangle , \langle - 8,32 \rangle$

Sketch the vectors u and w with angle between them and sketch the resultant. - $| \mathbf { u } | = 8 , | \mathbf { w } | = 3 , \theta = 80 ^ { \circ }$

Find the indicated vector. -Let $\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }$ . Find $6 \mathbf { u } + \mathbf { v }$ .

Find the missing parts of the triangle. -B = 44°20' b = 12.30 A = 31.26 If necessary, round side lengths to the nearest hundredth.

Determine the number of triangles ABC possible with the given parts. - $a = 32 , b = 65 , A = 79 ^ { \circ }$

Find the missing parts of the triangle. - $\begin{array} { l } \mathrm { B } = 104.3 ^ { \circ } \\\mathrm { a } = 298 \mathrm {~cm} \\\mathrm {~b} = 1324 \mathrm {~cm}\end{array}$ If necessary, round angles the nearest tenth and side lengths to the nearest $\mathrm { cm }$ .

Draw a sketch to represent the vector. Refer to the vectors pictured here. $Draw a sketch to represent the vector. Refer to the vectors pictured here. - \frac { 1 } { 2 } a A) B)$ - $\frac { 1 } { 2 } a$

Solve the problem. -Two ships leave a harbor together traveling on courses that have an angle of 129° between them. If they each travel 505 miles, how far apart are they (to the nearest mile) ?

Find the indicated vector. -Let $\mathbf { u } = \langle 6 , - 8 \rangle$ . Find $9 \mathbf { u }$ .

Determine the number of triangles ABC possible with the given parts. -b = 42, c = 52, B = 106°

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -a = 13.6 cm b = 18.4 cm C = 15.3 cm

Exam 7: Applications of Trigonometry and Vectors

Draw a sketch to represent the vector. Refer to the vectors pictured here. -a + (c + d)

Solve the problem. -A solar reflector is made using 29 identical triangular-shaped mirrors, each having sides 1.7 meters, 1.9 meters, 1.1 meters. What is the total surface area of the reflector (to the nearest square Meter) ?

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - a=6.3in.b=13.6in.c=15.3in.\begin{array} { l } a = 6.3 \mathrm { in } . \\b = 13.6 \mathrm { in } . \\c = 15.3 \mathrm { in } .\end{array}a=6.3in.b=13.6in.c=15.3in.​

Determine whether there is sufficient information for solving a triangle, with the given combination of angles and sides, by the law of sines. -b, B, and c

Write the vector in the form ai + bj. --5, 6

Solve the problem. -A painter needs to cover a triangular region 61 meters by 69 meters by 72 meters. A can of paint covers 70 square meters. How many cans will be needed?

Find the dot product for the pair of vectors. --13, 10 , 0, 9

Determine whether the pair of vectors is orthogonal. - ⟨−8,−1⟩,⟨−8,32⟩\langle - 8 , - 1 \rangle , \langle - 8,32 \rangle⟨−8,−1⟩,⟨−8,32⟩

Sketch the vectors u and w with angle between them and sketch the resultant. - ∣u∣=8,∣w∣=3,θ=80∘| \mathbf { u } | = 8 , | \mathbf { w } | = 3 , \theta = 80 ^ { \circ }∣u∣=8,∣w∣=3,θ=80∘

Find the indicated vector. -Let u=3i,v=i+j\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }u=3i,v=i+j . Find 6u+v6 \mathbf { u } + \mathbf { v }6u+v .

Find the missing parts of the triangle. -B = 44°20' b = 12.30 A = 31.26 If necessary, round side lengths to the nearest hundredth.

Determine the number of triangles ABC possible with the given parts. - a=32,b=65,A=79∘a = 32 , b = 65 , A = 79 ^ { \circ }a=32,b=65,A=79∘

Find the missing parts of the triangle. - If necessary, round angles to the nearest degree and give exact values of side lengths.

Draw a sketch to represent the vector. Refer to the vectors pictured here. - 12a\frac { 1 } { 2 } a21​a

Solve the problem. -Two ships leave a harbor together traveling on courses that have an angle of 129° between them. If they each travel 505 miles, how far apart are they (to the nearest mile) ?

Find the indicated vector. -Let u=⟨6,−8⟩\mathbf { u } = \langle 6 , - 8 \rangleu=⟨6,−8⟩ . Find 9u9 \mathbf { u }9u .

Determine the number of triangles ABC possible with the given parts. -b = 42, c = 52, B = 106°

Find the area of triangle ABC with the given parts. Round to the nearest tenth when necessary. -a = 13.6 cm b = 18.4 cm C = 15.3 cm

Find the missing parts of the triangle. Round to the nearest tenth when necessary or to the nearest minute as appropriate. - $\begin{array} { l } a = 6.3 \mathrm { in } . \\b = 13.6 \mathrm { in } . \\c = 15.3 \mathrm { in } .\end{array}$

Determine whether the pair of vectors is orthogonal. - $\langle - 8 , - 1 \rangle , \langle - 8,32 \rangle$

Sketch the vectors u and w with angle between them and sketch the resultant. - $| \mathbf { u } | = 8 , | \mathbf { w } | = 3 , \theta = 80 ^ { \circ }$

Find the indicated vector. -Let $\mathbf { u } = 3 \mathbf { i } , \mathbf { v } = \mathbf { i } + \mathbf { j }$ . Find $6 \mathbf { u } + \mathbf { v }$ .

Determine the number of triangles ABC possible with the given parts. - $a = 32 , b = 65 , A = 79 ^ { \circ }$

Draw a sketch to represent the vector. Refer to the vectors pictured here. $Draw a sketch to represent the vector. Refer to the vectors pictured here. - \frac { 1 } { 2 } a A) B)$ - $\frac { 1 } { 2 } a$

Find the indicated vector. -Let $\mathbf { u } = \langle 6 , - 8 \rangle$ . Find $9 \mathbf { u }$ .