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mancubit

Why is this true? (trigonometry)

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[attachment=2137:cosAngles.png]

i am currently examining some geometrical code and cant figure out why this is true and what trigonometry is behind this given equation.
Basically its about obtaining gamma, and the equation does the following

[s](cos(alpha) * a + cos(beta) * c) / b = gamma[/s]
edit: right formula: (cos(alpha) * a + cos(beta) * c) / b = cos(gamma)

Note the red lines are parallel

can someone explain whats behind that, why is that true?

feeling kinda dumb asking this, but i just cant get my head around that..

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I don't think that is true. Are you sure you didn't forget anything in the formula?

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sorry - you are right, i forgot that its actually cos(gamma) - i corrected it in the original post

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Hmmm... I would have quoted your original post if I knew you were going to change it...

I think I can figure this one out, but I'll need a little while to brush up on my plane geometry.

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I got it. It might be easier to see with a picture where beta is less than 90 degrees. What you do is measure the projection of a, b and c into the red direction. You'll get that the length of the projection of a plus the length of the projection of c should be equal to the projection of b. Even if beta is more than 90 degrees, the cosine will be negative and things will still work out.

You can then divide the whole thing by b and you'll get your formula.

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aaah makes sense!
thank you so much, you really helped me with this!

btw: i reedited the original post and striked the original formula out

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