Find the constant unknown angle of triangles series

[asanka000]

http://a.imageshack.us/img715/8526/paint2.jpg

there are 2 triangles. in these triangles r1,a,theta1 r2,a,theta2 are given. x1 and x2 are unknown. also the angle k is same for both triangles. i need to find this k. also i have data to draw series of tingles like these 2(i know r3,theta3,a ...etc). and all of them have the angle k. how to find it??

 

[Gear.0]

You can use the law of sines and the law of cosines.

http://en.wikipedia.org/wiki/Law_of_sines
http://en.wikipedia.org/wiki/Law_of_cosines

You can find the x's directly by using the law of cosines. Then once you know that side you can use x and theta, to find K with the law of sines.

 

[asanka000]

You can use the law of sines and the law of cosines.

http://en.wikipedia.org/wiki/Law_of_sines
http://en.wikipedia.org/wiki/Law_of_cosines

You can find the x's directly by using the law of cosines. Then once you know that side you can use x and theta, to find K with the law of sines.

how to find x from cosine rule. to apply this rule, it needs an angle inside triangle. but i don't know any angle. theta is the angle to a from x axis

 

[Gear.0]

Ah I see. I apologize for missing that.

You mean that theta is the angle between the x-axis and r1 right? You said it's from x-axis to a, but the picture you drew shows it going from x-axis to r1.

Either way I think it can't be solved. I am getting the feeling that you are leaving out some details that are subtle so you don't think they are important, but in fact are vital to solving this.

You see, if theta is the angle from x-axis to r1 then there is absolutely no restrictions on the angle of the a vectors. For example, in the first triangle, the leg 'a' could be located anywhere between theta1 and theta2 which would completely change the values of x1 and K.
Basically theta1 and theta2 only give you information about the location of the triangles, they don't tell you anything about the triangles sides or angles without additional information.

So basically all three angles are unknown, and 1 side is unknown. You cannot solve a triangle with only 2 knowns.

Try to give us more details, If you could write the exact problem you are working from that would be very helpful.

 

[asanka000]

any other ideas??

 

[Gear.0]

I am positive that without more information this cannot be done.
Do you agree with me that each triangle has 2 knowns and 4 unknowns? Then it can't be solved.

Just look at the picture. Let's call the angles which are at the origin B1 and B2, etc...
The easiest way to see what I'm talking about is to answer the question:
If you change B1 does K change?
I know you want K to be a constant, but you also want all of the angles to be constant, however this exercise will help you to understand what depends on what.
So if you change B1, you should be able to see that K must also change.

Ok... now there is absolutely no restraints on B1.. it can be anything right? So how can you possibly find K if K depends on B1 which is unknown?

I am pretty sure you are leaving information out which is more common considering that I don't think this is a homework problem.. So what is this for?

For example, you need a series.. well it would be impossible for you to have an infinite amount of triangles around the origin like that, so how many triangles do you need? That would put an upper limit on the B angles.
There's little things like that, which I'm pretty sure you are leaving out, we need more information to solve this.