difference of angles?

E

excess-thoughts

New member
Joined
Jun 27, 2006
Messages
4
Hello there everyone... I could really use some help with a question. There's just this one problem that I can't seem to get through... It's difficult to explain, so here is a graphic:

1519558857534825285_th.jpg


Okay, what I need is an equation that allows me to solve for the angle '?' You're given the values of a, b, c, d and theta, all of which are elements of real numbers. I'd appreciate any help that you could lend me. Thanks.

- Scott
 
I think the red bit is the angle "theta" and the blue bit is the angle "?", but I'm afraid the rest is too small for me to make out. Could you reply with a bigger version, please?

Thank you.

Eliz.
 
I'm sorry about that, I was in a bit of a rush to get it drawn up... I never even stopped to consider whether it would be readable... I've made a larger version, here's hoping that it's a bit better...

And thank you for the help =)

 
Thank you for the enlarged graphic! :D

Are "A, B, C, and D" the same as (from your original post) "a, b, c, and d"? Do the parentheses and commas indicate that A, B, C, and D are x,y-coordinates of points, so (C, D) = (0, 0), the origin? (This is what it looks like to me, anyway.) Is there any other information provided? Any instructions, other than "somehow find these values"?

Thank you.

Eliz.
 
*smiles* Sorry, I really should have taken my time when I wrote the first post.

Okay, the values a and b are the x and y cooridinates of any given point... The same goes for c and d... which doesn't nessecarily have to lie on the origin. I'm afraid that this wasn't an assigned question, so it came with no instructions...

I was in the middle of making a computer program when this problem presented itself to me. For the life of me I can't seem to figure it out.

Values A, B, C, D, are all elements of real numbers, while theta is any angle in degrees....

What I actually need is a way to solve for the angle '?' given the values A, B, C, D, and theta. As this isn't an assigned question, I'm not even sure if it is possible to do... either way, this sin't a matter of life or death. I'd appreciate any help that you could give me, but please don't loose any sleep over it.

I hope that it was clear enough... odds are my explanation was still a bit convoluted. Please feel free to ask anything else that you're not clear on.

- Scott
 
If (C, D) isn't the origin, how does this point relate to the rays? Does the line through (A, B) and the origin continue on? That is, is the first ray (counting anti-clockwise from the positive x-axis) on the same line as the third ray?

Thank you.

Eliz.
 
Assuming that the line from (A,B) through (C,D) to the circumference is
a straight line, then it's easy enough:

the left portion of the BLUE(!) angle = theta - 90

now for the right portion, which is same as the angle underneath it:
1: complete right triangle with point (C,B)
2: you now have a right triangle with legs = C-A and D-B
3: so you now can easily calculate the angle at (C,D)

BLUE angle = angle at (C,D) + theta - 90

That's as clear as I can make it, since you did not label ALL the points on your diagram...
 
One could also use the slope of the line through (A,B) & (C,D).
\(\displaystyle \L
\Theta - ? = \arctan \left( {\frac{{D - B}}{{C - A}}} \right)\)
 
You must log in or register to reply here.
Top