Solve for angle and a length of a triangle

[ClemAmelia]

So I have a triangle where I have two of the lengths and need to solve for the last length and the angle (unknown if right angle/acute etc). Is this possible to do with simultaneous equations or otherwise, and if so how would you go about doing it? I can get the x and y coordinates, but its for a program that will use this hundreds of times and it isn't easy to get the coordinates so was hoping for a easier solution.

 

[Steven G]

I am sorry but this is not a forum where we solve problems for students. We prefer that the student solves their own problem with help from forum helpers.

So please post back with your work so we can see where you need help. Also include a labelled diagram.

You say that you have a triangle where I have two of the lengths and need to solve for the last length and the angle (unknown if right angle/acute etc). Which angle are you referring to? Do you know any of the other angles???

 

[ClemAmelia]

Ah sorry, promise this isn't homework! If you can point me in the right direction that would be much appreciated! I'm trying to compare rotation invariant solutions for fingerprint recognition, this is an algorithm I'm trying to implement: for the following diagram, I'm trying to calculate ThetaM, with the lengths dmi and dmj (both are known) . A solution to finding ThetaM is attached, which needs a length that I don't have (dij). Apologies for the image quality, my computers graphics card is slightly broken so had to take a photo with my phone to upload.

 

[lev888]

The 2 sides can have any angle between them. Make a V sign with your fingers. That's your model. Now bring the fingers together. Same sides, different angles, different 3rd side. Not enough info to solve it.