Check out part 1 here: Measuring diaognals without Sine Law - this is an equivalent construct.
Suppose we construct a triangle with lengths $5,7,\sqrt{32}$ on the cartesian plane. Using Heron's Area formula, we can verify A = $(0,4)$ (ie: height = 4).
Now we rotate triangle around $(4,0)$ so that one corner touches the Y-axis (ie: second figure).
Question: what is the new position of A$(x,y)$? The top figure is easily solved, but the 2nd figure requires quadratic sums with two possible answers. (see Part 1 link above).
note: law of Cosines is the generalization of Pythagoras Theorem. However, we aren't using this rule yet.
Well, I don't even see why trig has to be involved in this question. If you want to find the coordinates, use the distance formula:
between $(0,\sqrt{33})$ and $(x,y)$:
$\sqrt{x^2 + (y-\sqrt{33})^2} = 25$
between $(x,y)$ and $(4,0)$
$\sqrt{(x-4)^2 + y^2} = 32$
solve for x and y.