So if I have a hypotenuse and a ratio between the opposite and adjacent, Can I find Theta? I realize that tan(x) = o/a yet the thing I forgot how to do was to take opposite/adjacent and solve for x…I would know what the tangent of x is then, but how can I go back and figure out what x is? I have a calculator here, and I can’t figure it out…
If the tangent of theta is O/A, then figure O/A, then use inverse tan to find theta.
Inverse of trig functions is similar to roots. If X squared plus Y squared equal Z squared; then square X and Y; add; then take square root of the sum to get Z.
Look at a triangle which you know the angles of and check your formula.
I’m not sure what NinetyWt is getting at, exactly, with his second paragraph, but the inverse of the tangent function is called the arctangent function. If all you want to do is calculate it, well, it’ll be there, in some fashion, on any decent calculator, marked as “arctan” or “tan^-1” or some such thing. Pass it tan(x) as an argument, and it’ll give you an output in the range (-pi/2, pi/2) which differs from x by a multiple of pi (if x is in that range already, then you’ll get x).
Elaborating on the above, where you have an equation, you can solve by doing the same thing to both sides. So given
tan(x) = o/a
you take arctangents (tan[sup]-1[/sup], the inverse function of tangent) thus:
tan[sup]-1/sup = tan[sup]-1/sup
But tan[sup]-1/sup just equals x (the whole idea of an inverse function: if you apply a function to an argument, and then the inverse function to the result, you get back the argument) so this simplifies to:
x = tan[sup]-1/sup
Indistinguishable is right as to the general case of arctangent, but here you have the specific case that the angle must be less than 90 degrees as you are stated to be solving a right-angled triangle and so his answer is more all-embracing than you actually need.
Nitpick: blah blah multiple values blah blah not well-defined blah blah blah mod n*pi blah blah Riemann sheets blah blah blah.
Absolutely, but in the simple case of a right-angled triangle, which is what the OP was asking about… Of course tan(x) has an inverse function only for certain values of x, but blethering on about domains and image sets was only going to confuse the issue. 
For the practical answer, on most calculators, you get the inverse tan function by pushing an “inverse” (or “alternate” or “2nd” or “shift” or some such) button, followed by the tan button.
Hilariously succinct :D.