What are the possibilities?

Reproduce the diagram on a piece of paper and answer the following questions. Provide the reasoning that justifies your answer in each case.

  1. Determine the measure of .
  2. Find the lengths of BC and AC.
  3. Slide points P and Q a bit. Assume that Q is able to move infinitely to the right. Then determine the range of possible lengths for CP and CQ.
  4. Sketch two possible triangles which have a side 7 units in length adjacent to a angle and a side 8 units in length opposite the same angle. If this is not possible, explain why.