Deceiving Simple Geometry Question

[hobbes33]

Here's a simple looking geometry question, but I can't seem to solve it.
But according to scale models, there is a unique answer for BC.

Equations with Pythagoras' theorem or cosine rule always seems to end up in an illegible pile of mess.

Does anyone has any idea how to go about solving the question?

 

[slider142]

You have 7 unknown angles and there are 7 linear independent equations relating them, so the solution is unique. You can use the angles and trigonometry to find BC.

 

[hobbes33]

Thanks for pointing out that info.

But isn't there another way to solve this question rather than to solve a 7 variable simultaneous equation? Most variables are not linear combination of each other too, so I doubt the 7 equations are practically reducible.

 

[alligatorman]

I was able to find a solution using the Law of Sines on triangle AYX, namely on angles AYX and YAX

edit:
nevermind, i drew the picture incorrectly.

 

[hobbes33]

In case anyone wants to check, the answer should be around 3.6 using a scale model.

By using a software to digest some of the equations i threw in, the answer comes out to approximately 3.580181.

But of course, the equations are too long for someone to solve by hand. I think someone must have a better method than me.