Question

Use compass directions to describe the direction of the vector. The diagram is not drawn to scale.

Answer 1

You start by facing directly west

Answer 2

Then you turn 41 degrees south

Answer 3

to get to the direction you want to face

Answer 4

So you can describe this direction as 41 degrees south of west

Answer 5

so all I will have to write is 41 degrees south of west?

Answer 6

pretty much

Answer 7

oh okay thank you. Could you help me with another question?

Answer 8

ok one more

Answer 9

A boat is crossing the river as shown. To the nearest tenth of a degree, find the angle at which the boat must head upriver in order to travel directly across the river. The diagram is not drawn to scale.

Answer 10

the tangent of the angle x is 5/14

so

tan(x) = 5/14

Answer 11

to isolate the x, we apply the arctan to both sides

tan(x) = 5/14

arctan[ tan(x) ] = arctan(5/14)

x = arctan(5/14)

Answer 12

70.3° north of west
19.7° north of west
19.7° south of west
70.3° south of west

these are the answer selections

Answer 13

i think its c

Answer 14

now we use a calculator to get this

https://www.google.com/search?hl=&q=arctan%285%2F14%29+in+degrees&sourceid=navclient-ff&rlz=1B3GGLL_enUS420US420&ie=UTF-8

Answer 15

how is it SOUTH?

the resultant is NORTH of the x axis

Answer 16

you had the degree measure correct though

Answer 17

it's 19.7 degrees north of west

Answer 18

oh Im sorry :( Im just having alot of trouble getting this. I thought it was south

Answer 19

no, it's north because otherwise, it's going with the current and it won't reach where it wants to go

Answer 20

it wants to go directly west

but the current is pushing it south

so it has to go 19.7 degrees north of west to compensate for the current...which will make them land at the destination directly west

Answer 21

Oh okay I will have to study more on this! If you would help me with one more that would be great but if you dont have time thats fine

Answer 22

I guess I could do one more, but I don't want to do everything

Answer 23

what's your question

Answer 24

Find the magnitude and direction of the vector. Round the length to the nearest tenth and the degree to the nearest unit. The diagram is not drawn to scale.

Answer 25

this is a right triangle

how do you find the hypotenuse?

Answer 26

if you're stuck, use the pythagorean theorem

a^2 + b^2 = c^2

Answer 27

a2 + b2 = c2

Answer 28

sorry my computer froze up

Answer 29

that's fine

Answer 30

a^2 + b^2 = c^2

6^2 + 4^2 = c^2

solve for c

Answer 31

so i add like terms?

Answer 32

6^2 = ??

Answer 33

I dont know? Do I add 6^2 and 4^2

Answer 34

6^2 = 6 squared

Answer 35

6^2 = 6 squared = 6*6 = ??

Answer 36

36

Answer 37

4^2 = ??

Answer 38

16

Answer 39

6^2 + 4^2 = c^2

36 + 16 = c^2

Answer 40

52

Answer 41

52 = c^2

c^2 = 52

Answer 42

c = ??

Answer 43

am I supposed to do 52 times 52

Answer 44

what undoes a square exponent

Answer 45

if you square 7 to get 49

how do you undo that?

Answer 46

i dont know :(
divide it maybe?

Answer 47

square roots undo squaring

Answer 48

7^2 = 49


sqrt(49) = 7

Answer 49

so if

c^2 = 52

then

\[\Large c = \sqrt{52}\]

now simplify the square root

Answer 50

13

Answer 51

\[\Large \sqrt{52} = \sqrt{4*13}\]


\[\Large \sqrt{52} = \sqrt{4}*\sqrt{13}\]


\[\Large \sqrt{52} = \sqrt{2^{2}}*\sqrt{13}\]


\[\Large \sqrt{52} = 2\sqrt{13}\]

Answer 52

So

\[\Large c = \sqrt{52}\]

turns into

\[\Large c = 2\sqrt{13}\]

Answer 53

okay I understand that now! so is that it?

Answer 54

that's it for the magnitude

Answer 55

that's the exact magnitude, you can use a calculator to find the approximate magnitude if you wanted

Answer 56

what about the direction?

Answer 57

tan(x) = opp/adj

tan(x) = 4/6

x = arctan(4/6)

x = ??

Answer 58

I honestly have no clue? am i supposed to divide 4 by 6

Answer 59

use the calculator i used before

Answer 60

type

"arctan(4/6) in degrees"

without quotes into google

Answer 61

what am I supposed to enter?

Answer 62

google will act like a calculator and spit out the answer

Answer 63

33.6900675 degrees

Answer 64

good, so it's roughly 33.69 degrees north of east

Answer 65

oh okay So now is the question complete? Ill go back and look

Answer 66

yes you found the magnitude and direction, so you're done

Answer 67

oh it wants the length and degree to the nearest tenth

Answer 68

it says find the direction of the vector... we did that right?

Answer 69

so

sqrt(52) = 7.2

33.69 ---> 33.7

Answer 70

Length = 7.2 units

Direction: 33.7 degrees north of east

Answer 71

yeah we did it correctly

Answer 72

okay thank you!

Answer 73

np