Deck 7: Applications of Trigonometry

Question 1

Find the magnitude of vector v.
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Answer 1

$\| \mathbf { v } \| = 5$

Question 2

Find the angle between the vectors u and v. $\mathbf { u } = \cos \left( \frac { \pi } { 3 } \right) \mathbf { i } + \sin \left( \frac { \pi } { 3 } \right) \mathbf { j }$ , $v = \cos \left( \frac { 3 \pi } { 4 } \right) i + \sin \left( \frac { 3 \pi } { 4 } \right) j$ ​

Answer 2

$75 ^ { \circ }$

Question 3

Use the vectors $\mathbf { u } = \langle 4,3 \rangle$ , $\mathbf { v } = \langle - 3,2 \rangle$ to find the indicated quantity. State whether the result is a vector or a scalar.
​ $( \mathbf { u } \cdot \mathbf { v } ) \mathbf { v }$ ​

Answer 3

$\langle 18 , - 12 \rangle$ ; vector

Question 4

Given A = 10 $\circ$ , b = 10 and c = 8, use the Law of Sines to solve the triangle (if possible) for the value of c. If two solutions exist, find both. Round answer to two decimal places.

Question 5

Two ocean liners leave from the same port in Puerto Rico at 10:00 a.m. One travels at a bearing of N 50°W at 12 miles per hour, and the other travels at a bearing of S 53°W at 14 miles per hour. Approximate the distance between them at noon the same day. Round your answer to two decimal places.
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Question 6

A straight road makes an angle, A, of 16° with the horizontal. When the angle of elevation, B, of the sun is 59°, a vertical pole beside the road casts a shadow 7 feet long parallel to the road, see figure. Approximate the length of the pole. Round answer to two decimal places.

Question 7

Use DeMoivre's theorem to find the indicated roots of the complex number.
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Square roots of $11 \left( \cos 120 ^ { \circ } + i \sin 120 ^ { \circ } \right)$ .
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Question 8

Given a = 12, b = 11, and c = 10, use the Law of Cosines to solve the triangle for the value of B. Round your answer to two decimal places.
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Question 9

Divide the complex numbers below and leave the result in trigonometric form. $$\frac { 2 \left( \cos 160 ^ { \circ } + i \sin 160 ^ { \circ } \right) } { 9 \left( \cos 290 ^ { \circ } + i \sin 290 ^ { \circ } \right) }$$ ​

Question 10

Use vectors to find the measure of the angle at vertex B of triangle ABC, when $A = ( 5,2 )$ , $B = ( - 4,1 )$ , and $C = ( - 1 , - 3 )$ . Round answer to two decimal places.
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Question 11

Use the law of Cosines to solve the given triangle. Round your answer to two decimal places.
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a = 10, b = 5, C = 113°
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Question 12

A 800-pound trailer is sitting on an exit ramp inclined at 33° on Highway 35. How much force is required to keep the trailer from rolling back down the exit ramp? Round your answer to two decimal places.
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Question 13

Find the fifth roots of the following complex number. Express the root(s) in trigonometric form.
​ $$- \frac { 3125 } { 2 } + \frac { 3125 } { 2 } \sqrt { 3 } i$$ ​

Question 14

Find u + v.
​ $\mathbf { u } = \langle 5,1 \rangle , \mathbf { v } = \langle 1,6 \rangle$ ​

Question 15

Given A = 33°, b = 13, and c = 7, use the Law of Cosines to solve the triangle for the value of a. Round your answer to two decimal places. Figure not drawn to scale