I finding resultants using sine/cosine law

[EddyBenzen122]

Homework Statement

None.

Relevant Equations

None.

I need help finding the resultant with vectors: 37.5N[NE] and 45N[21° S of E]
I just don't know a way to find the angles within this triangle to help me get the resultant, so can anybody help me out?

 

[kuruman]

According to forum rules, you must show some effort towards the solution before you get help. Please do so. Also, sine/cosine law is not an equation.

 

[EddyBenzen122]

According to forum rules, you must show some effort towards the solution before you get help. Please do so. Also, sine/cosine law is not an equation.

This is the best I could! I only need someone to help me figure out how I could find the angles within the triangle given so that I could find the resultant on my own.

 

[haruspex]

This is the best I could! I only need someone to help me figure out how I could find the angles within the triangle given so that I could find the resultant on my own.

Project the first vector out beyond the tail of the second one. What is the angle between them?

 

[EddyBenzen122]

Project the first vector out beyond the tail of the second one. What is the angle between them?

Is this what you mean?

 

[haruspex]

Is this what you mean?
View attachment 289612

Yes, I'm asking what the value of theta is in that diagram. But it does not depend on the force magnitudes, only on their directions.

 

[robphy]

You could, but you don't need to work with that triangle's angles to get the resultant.
The resultant is the vector-sum using the tip-to-tail "treasure map" method.
You are given enough information to get the x- and y-components of each given vector, and thus get the resultant.
Then you could use the resultant to get (say) the angle theta between that resultant and the first vector [using the dot product or law of cosines].

 

[neilparker62]

 

[EddyBenzen122]

View attachment 289732

I was able to solve it using the idea of interior alternates to find the angle opposite to the resultant and then I found the resultant using cosine law afterwards. That's all I really need for help, thanks, everyone!

 

[robphy]

I was able to solve it using the idea of interior alternates to find the angle opposite to the resultant and then I found the resultant using cosine law afterwards. That's all I really need for help, thanks, everyone!

In my experience, many introductory students don’t know the law of cosines (which comes from the dot product of two vectors). So, congratulations.

To me, the problem suggests the tip-to-tail method for adding vectors graphically, but suggesting (from what it gave as given) one should add using components.

For two forces, either method (law of cosines or vector components) works well if one can construct the necessary quantities.
However, for more than two vectors, using vector components is likely easier and more direct.
(This method can be implemented in a computer program more easily than using the law of cosines several times in progression .)
So, learning to use components will likely be useful.

My $0.02.