## Triangle Point Translation Problem (with picture)

Trigonometric ratios and functions, the unit circle, inverse trig functions, identities, trig graphs, etc.

### Triangle Point Translation Problem (with picture)

Hello all, I am having trouble with a trig problem, and was hoping I could get some help. Here's an image that should make it easier to understand what I need to do.

I have the coordinates of the three points, A, B, and C for the blue triangle, and as such, I can find the side lengths and inner angles easily using Pythagorean's Theorem and the Law of Cosines. What I need to be able to do is this:

Given a new angle between Pt A and Pt C (where Pt B is the vertex), how much do I need to translate Pt B on the y axis to form this new angle. The new Pt B will have the same x value as the old Pt B, only the y value must change. Another way of looking at it is, what is the length of the Red line in the picture above? I have been racking my brain trying to figure this out, and I am no closer to a solution than I was a day ago. Please help!!

tavi033

Posts: 2
Joined: Wed May 01, 2013 8:05 pm

### Re: Triangle Point Translation Problem (with picture)

I'm not clear on what you're trying to do. Are you saying that you'll be moving Point B directly upward, with Points A and C remaining the same, and you're needing to find a formula for the length of the red "shift" line in terms of the new angle at B's new location?

stapel_eliz

Posts: 1799
Joined: Mon Dec 08, 2008 4:22 pm

### Re: Triangle Point Translation Problem (with picture)

Yes, exactly.

While I am still interested in an answer, I think I found another way to find what I want.
tavi033

Posts: 2
Joined: Wed May 01, 2013 8:05 pm