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There are 4 unknowns constants: a,b,c,p. The variable is phi and the result is d.

For phi={13,23,45,73} the results are d={32.08754292290807,32.1136624112758,32.1728430675844,32.2430287624866}

The equation is:

(c/0.3048*((1+(a*p/(b*c))*(sin(phi*pi/180))^2))/sqrt(1-sqrt(1-b^2/a^2)*
((sin(phi*pi/180))^2))) = d

How can I solve it in Mathematica?

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If I decipher your parentheses correctly, this is just a second order algebraic equation in u if you set u=Sin[phi]^2. So you may directly define a function

f[a_,b_,c_,p_] := Block[{A,B,C,Delta,U},
                         A=...;B=...;C=...;Delta=Sqrt[B^2-4*A C];
                         U=...;
                         phi=ArcSin[Sqrt[U]];]

which first solves the equation in u, then takes the arcsin.

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  • $\begingroup$ Note that C is protected! $\endgroup$ – sebhofer Oct 31 '12 at 16:11
  • $\begingroup$ @sebhofer It's inside a Block :) $\endgroup$ – rm -rf Oct 31 '12 at 16:18
  • $\begingroup$ @rm-rf Damn ... $\endgroup$ – sebhofer Oct 31 '12 at 16:37
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    $\begingroup$ @rm-rf clker.com/cliparts/G/b/l/l/m/l/alphabet-block-c-md.png $\endgroup$ – Dr. belisarius Oct 31 '12 at 17:54
  • $\begingroup$ Thank you, I' m able to do second order algebraic equation but I don't known how to solve it. Can you provide exact code (or How can I put there all 4 solutions i.e. (For phi={13,23,45,73} the results are d=32.08754292290807,32.1136624112758,32.1728430675844,32.2430287624866})) Thank you in advance. Milos $\endgroup$ – Milos Oct 31 '12 at 18:20

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