Wacky trig. I am totally lost.

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SUMMARY

The discussion centers on solving a problem involving intersecting triangles, specifically finding the variable x. The key insight is that the angle opposite the side measuring 12 is twice that of the side measuring 6, leading to the conclusion that the tangent of the angle opposite 12 is twice the tangent of the angle opposite 6. The solution emphasizes the use of similar triangles rather than traditional trigonometric functions to derive relationships and solve for x.

PREREQUISITES
  • Understanding of similar triangles
  • Basic knowledge of trigonometric functions
  • Familiarity with tangent ratios
  • Ability to manipulate algebraic expressions
NEXT STEPS
  • Study the properties of similar triangles in geometry
  • Review the definitions and applications of tangent functions
  • Practice solving problems involving angle relationships in triangles
  • Explore inverse trigonometric functions and their applications
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Students studying geometry, particularly those struggling with triangle properties and relationships, as well as educators looking for examples of applying similar triangles in problem-solving.

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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.
 
Last edited:
Oh. Thanks for the tip. I got it now.
 

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