Tricky Triangle Problem

Is the answer here D? How do you figure this out? What concepts do I need to study to get this?

If you flatten the triangle (move point Q down), maybe x will get bigger, but if you stretch it (move point Q up), y will get bigger, since we don’t know the height we might not be able to tell here. Not sure if that makes sense.

Hmm I think so, so what you’re basically saying is that you need to know the height in order to tell what x and y are, and the height needs to be perpendicular with 90 degrees at the base. I guess at that point, the question would need to point out that the triangle is drawn to scale.

The strategy is brute force. If you can’t apply a formulae then it’s a good idea to put in some sensible numbers and play around to get some hints. I made two triangles:

  1. Let triangle QSR be a right isosceles triangle. Here x = y Therefore C is possible
  2. Now draw it such that y is 120 degrees. Clearly x is much smaller. Hence B is possible.

With the given information you can confidently say that it must be option D. Cannot be determined with the given information.