Question

Help please,
A force of 164 pounds makes an angle of 74 degrees 39 minutes with a second force. The resultant of the two forces makes an angle of 34 degrees 12 minutes to the first force. Find the magnitudes of the second force and of the resultant.
(Please show steps, I have no idea how to do the steps please explain.)

Answer 1

that is the diagram of whats going on i think

Answer 2

ok thats an equivalent drawing

Answer 3

I'm more confused with steps the drawing part is fine

Answer 4

A force of 164 pounds makes an angle of 74 degrees 39 minutes with a second force. The resultant of the two forces makes an angle of 34 degrees 12 minutes to the first force. Find the magnitudes of the second force and of the resultant.
(Please show steps, I have no id

F_1 = < 164 cos(0) , 164 sin(0)
F_2 = < |F_2| cos (74 + 39/60) , |F_2| sin( 74 + 39/60)>

Answer 5

$$ \large \rm {
\vec F_1=( 164 cos(0~^o) , 164 sin(0~^o)) = (164, 0)
\\\vec F_2 = ( |F_2| cos (74~^o + 39/60~^o) , |F_2| sin( 74~^o + 39/60~^o))
\\ Resultant = \vec F_1 + \vec F_2\\
\\ = ( 164,0) + ( |F_2| cos (74~^o +\frac{39}{60}~^o) , |F_2| sin( 74~^o + \frac{39}{60}~^o))\\
= ( 164+ |F_2| cos (74~^o + \frac{39}{60}~^o),~ 0 + |F_2| sin( 74~^o + \frac{39}{60}~^o))\\
= ( 164+ |F_2| cos (74~^o + \frac{39}{60}~^o), ~|F_2| sin( 74~^o + \frac{39}{60}~^o))\\
\\ \theta = arctan (\frac{ |F_2| sin( 74~^o + \frac{39}{60}~^o))}{164+ |F_2| cos (74~^o + \frac{39}{60}~^o)}
\\ \therefore \\\\
34+\frac{12}{60} =arctan (\frac{ |F_2| sin( 74~^o + \frac{39}{60}~^o))}{164+ |F_2| cos (74~^o + \frac{39}{60}~^o)}
} $$

Answer 6

solve for |F_2|

Answer 7

34.2 = 15.14 ?

Answer 8

take tan of both sides

Answer 9

88.33= 15.14 is what I'm getting

Answer 10

oh so F2= 121.4

Answer 11

34 degrees 12 minute = 34 + 12/60 = 34.2 degrees

74 degrees and 39 minutes = 74 + 39/60 degrees = 74.65 degrees

Answer 12

thats correct

Answer 13

$$ \Large \rm { Resultant = \sqrt{|F_1|^2 + |F_2|^2} } $$

Answer 14

my book says that the second force has a magnitude of 142 lb

Answer 15

alright

Answer 16

now it works
http://www.wolframalpha.com/input/?i=solve+%2834.2+degrees+%29+%3D+arctan%28x*sin%28+74.65+degrees%29+%2F+%28+164+%2B+x+*+cos%2874.65+degrees%29+%29%29

Answer 17

☺

Answer 18

got it written

Answer 19

now see if you can find the magnitude of the resultant

Answer 20

I got 244 but I have one a question on using the line of sines how would I find angles ACB and ABC of the figure from this problem?

Answer 21

you want to use law of sines?

Answer 22

yes

Answer 23

so are you ok with the magnitude of the resultant?

Answer 24

yes

Answer 25

what idd you get

Answer 26

244

Answer 27

yes same here