Question

If sin A = .5 and cos A = .866 then what is tan A to the nearest thousandth

Answer 1

Somewhere in a table of trig-function definitions that you have somewhere,
it mentions that

tan(a) = sin(a) / cos(a).

So it must follow that

tan(A) = (0.500) / (0.866) = 0.577 (rounded)