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Solving formula with unknown in two trigonometric functions?

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Hello,

I try to solve a somewhat complex geometric problem and found a formula to solve that problem: tan(a)=(D-(d/cos(a)))/t

Problem is I'm looking for "a" but no online solver or any colleague I ask knows how to solve this equation for "a".
Now I found the answer trough approximation.
But this has just one unknown. Why can't anyone solve for it?

Any Ideas?
 Jan 10, 2014

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 #1
avatar+118654 
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Hi Lomsor,

tan(a)=(D-(d/cos(a)))/t

I assume that you want to make a the subject?
No I am out of ideas.

Are D,d and t constants? Do they have constraining values?
 Jan 10, 2014
 #2
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Yes I want to make a subject.

D,d and t are Natural numbers. They are known but.

The formula is for calculating the maximum angle a rod with diameter "d" can be tilted in a whole with diameter "D" with a material thickness of "t".

If D and d both are 22 for instance, the maximum angle would be 0.

For my problem D is 12mm, d is 10mm and t is 3mm. Trough aproximation (
t=(12-(10/cos(22)))/tan(22) I found the solution is 22 Degrees at a t of 3.006mm. So a pretty close aproximation
 Jan 10, 2014

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