The value of x − y is negative, and x and y are both positive. what can you conclude about the values of x and y?

x is approximately equal to 66.014536898

Step-by-step explanation:

You can solve this using the sine rule:

where a, b, and c are the sides of the triangle, and A, B and C are the angles opposite those sides.

But first, we need to know the angle of the corner opposite the one side that we do have the length of.  Fortunately, we can work that out, knowing that the angles inside a triangle will always add up to 180°.  We are already given two of them 59° and 90° , so the third is just 180 minus those two:

180° - 90° - 59°

= 31°

Now to find x, we simply apply the sine rule:

Note of course that the answer is not exactly 66.  If I plug 34 / sin(31) into a calculator, I get 66.014536898.  If you're getting a "wrong" on that answer, you might want to double check how they expect you to format it (e.g. rounded to the nearest tenth, hundredth, etc.)