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Here's the free-body diagram of a stupid physics problem I had:

http://img211.imageshack.us/img211/5081/triangleey9.png [Broken]

When going over this problem both my book and my lecturer say that [tex]\alpha = \theta[/tex] (they actually don't even mention [tex]\alpha[/tex]; they just write it as [tex]\theta[/tex] to begin with. I just wrote the [tex]\alpha[/tex] there myself) as if it's obvious and trivial. I don't see how it's obvious though. I had to draw out http://img233.imageshack.us/img233/9138/triangle2sz6.png [Broken] and figure that [tex]\beta+\alpha=90[/tex] and [tex]\beta+\theta=90[/tex] and therefore [tex]\alpha=\theta[/tex] which took me a few minutes to figure out.

My question is, when you see my first image (the physics one) do you immediatley see that that angle is equal to [tex]\theta[/tex]? Please tell me how you knew. I want to have this kind of intuition about things but I just don't see it. What relationships did you use? Is there another way to do it other than my alpha-beta thing?

http://img211.imageshack.us/img211/5081/triangleey9.png [Broken]

When going over this problem both my book and my lecturer say that [tex]\alpha = \theta[/tex] (they actually don't even mention [tex]\alpha[/tex]; they just write it as [tex]\theta[/tex] to begin with. I just wrote the [tex]\alpha[/tex] there myself) as if it's obvious and trivial. I don't see how it's obvious though. I had to draw out http://img233.imageshack.us/img233/9138/triangle2sz6.png [Broken] and figure that [tex]\beta+\alpha=90[/tex] and [tex]\beta+\theta=90[/tex] and therefore [tex]\alpha=\theta[/tex] which took me a few minutes to figure out.

My question is, when you see my first image (the physics one) do you immediatley see that that angle is equal to [tex]\theta[/tex]? Please tell me how you knew. I want to have this kind of intuition about things but I just don't see it. What relationships did you use? Is there another way to do it other than my alpha-beta thing?

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