Wacky trig. I am totally lost.

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The discussion revolves around solving a problem involving intersecting triangles and finding the variable x. The initial confusion stems from the application of trigonometric functions, leading to dependence on multiple variables. A key insight is recognizing that the triangle with a side of 12 has an angle that is twice that of the triangle with a side of 6, which relates to their similarity. The solution ultimately relies on understanding the properties of similar triangles rather than complex trigonometric calculations. The participant successfully resolves the problem after this clarification.
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Intersecting triangles.

Homework Statement



Find x

http://img177.imageshack.us/img177/3043/trighj0.png

Homework Equations


trig and inverse trig functions?

The Attempt at a Solution



I have no idea how to solve this. When I try and use the trig that I know to find the lengths, I also end up having to depend on other variables.

The only thing I was able to find out is that the angle opposite the 12 is twice the that of the 6.
 
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The TANGENT of the angle opposite 12 is twice the tangent of the angle opposite 6, if that's what you mean. But no trig necessary here. It's all similar triangles. Write down some relations you get from similarity.
 
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Oh. Thanks for the tip. I got it now.
 

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I picked up this problem from the Schaum's series book titled "College Mathematics" by Ayres/Schmidt. It is a solved problem in the book. But what surprised me was that the solution to this problem was given in one line without any explanation. I could, therefore, not understand how the given one-line solution was reached. The one-line solution in the book says: The equation is ##x \cos{\omega} +y \sin{\omega} - 5 = 0##, ##\omega## being the parameter. From my side, the only thing I could...
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