Relationship between angle gamma and alpha and beta

Demon117

So I feel like a complete moron for asking this. I have never been very strong in geometry so I wondered if a few math folks could help me out. I am just looking for the angle relationships of gamma, alpha, and beta. This is just a small piece of a much larger analysis that I am doing.

I know that beta and gamma are related by [itex]\gamma=\beta - \frac{\pi}{2}[/itex], so if someone could push me in the right direction in determining the relationship between gamma and alpha. Thanks in advance.

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hamsterman

Unless you excluded some condition, there is no relation between alpha and the other two. Any two right triangles could be composed like this.

Demon117

So you are telling me that I cannot describe the angle gamma in terms of its deviation from the horizontal plane? The plane on which the large triangle sits?

Office_Shredder

Take the point where the small triangle meets the big one (at angle gamma) and rotate the leg of the small triangle so that the location of angle gamma changes. You get different values of gamma without changing the value of alpha. So gamma cannot be solved in terms of alpha alone.