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#1




Geometry Problem
I ran into a very practical problem math building a gate this weekend. Basically I had two 2x4s running parallel a certain distance apart, and I wanted to cut a cross piece that for aesthetic reasons ran from one end to the other. This is obvious a simple SOHCAHTOA for a line, but for a beam of finite width it isn't so simple. I ended up solving it practically (physically do it, and measure), but now I can't make the math work and it is bothering me.
I end up with an equation, but it has two trig functions that I can't reduce with a trig identity, so it isn't directly solvable by an inverse trig function. It seems like it should have an obvious direct solution... 
#2




Re: Geometry Problem
θ = inverse sin((bc) / a)

#3




Re: Geometry Problem

#4




Re: Geometry Problem
Not the prettiest way, but a single trig identity and the quadratic equation will get you there:
Last edited by GeeTwo : 03112017 at 07:42 AM. Reason: Added open parenthesis on penultimate line 
#5




Re: Geometry Problem
Using symbols instead of text...
θ = sin⁻¹((bc) / a) 
#6




Re: Geometry Problem
Quote:
I probably knew this once upon a time, what does the other solution to that quadratic represent? 
#7




Re: Geometry Problem
...

#8




Re: Geometry Problem
Ether's solution is correct. Mine started out the same way but in the process I dropped / forgot to cross multiply the right side by cos theta.

#9




Re: Geometry Problem
Quote:
Last edited by GeeTwo : 03102017 at 07:50 AM. Reason: swapped a and b originally 
#10




Re: Geometry Problem
Quote:
I'm still a little surprised the solution is so complicated, I was sure I was missing something obvious and it was going to end up with something like Cesar's original post. 
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