# Thread: Solving a right triangle based upon linear constraints

1. ## Solving a right triangle based upon linear constraints

Before I start this is not a homework problem or some math I am having trouble understanding. This is just a limit of my knowledge finally winning after 2 weeks beacuse although i'm almost sure this problem is solvable and I have answers via trial an error I will not give up till I have an elegant solution. When several PHDs have no idea its time to ask people with more math in there backgrounds.

This problem has 3 stages with the last one being the true problem I have and the first two being simplifications i'm trying to use to get at the more complex final problem. I really hope this is not an impossible problem to solve other than by trial and error and I would likes the steps to get to a formula.

Solve for X given A, B
X is the entire bottom line not just the single dash

Solve for X given A,B,C

Solve for X given A,B,C,D

2. ## Re: Solving a right triangle based upon linear constraints

I am sure that I am not the only one here who would like to help you solve this, but any attempts at that are seriously hampered by your drawings. Can you please present them in the 'standard method', i.e. every point where two lines meet, assign a letter of the alphabet (capital letter). Then give auxiliary statements as to which lines are equal in length to various other lines and ditto with various angles. Plus, if any of those angles are 90°, then please state as such.

With sincere respect,
Al. / Skywave (June 16, 2017)

3. ## Re: Solving a right triangle based upon linear constraints

First, are we to assume that these are right triangles? If so, in regard to the first one, does the single tic mark on part of horizontal line and the vertical line mean that they are of equal length? Assuming all of that, let the length of the tic'ed segments be y. Since x is the length of the entire horizontal line, y= x- a. The Pythagorean theorem gives $\displaystyle B^2= x^2+ y^2= x^2+ (x- A)^2= x^2- 2Ax+ A^2$. Solve the quadratic equation $\displaystyle x^2- 2Ax+ A^2- B^2= 0$ for x.