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 $\gamma=\beta - \frac{\pi}{2}$, so if someone could push me in the right direction in determining the relationship between gamma and alpha. Thanks in advance.

 

[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]

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

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.

 

[CellCoree]

No need to feel like a moron for asking for help! Geometry can be a challenging subject for many. The relationship between gamma and alpha can be determined by using the fact that the sum of angles in a triangle is 180 degrees. Since we know that beta and gamma are related by \gamma=\beta - \frac{\pi}{2}, we can substitute this into the equation for the sum of angles in a triangle: \alpha + \beta + \gamma = 180. This gives us \alpha + \beta + (\beta - \frac{\pi}{2}) = 180. Simplifying this equation gives us the relationship between gamma and alpha as \gamma = \frac{\pi}{2} - \alpha. This means that gamma and alpha are complementary angles, meaning they add up to 90 degrees. I hope this helps with your analysis!