Interactive Trigonometry Question 1

In the diagram, AB is fixed at length 10. Find the lengths of 1) AC 2) BC 3) BD 4) AC 5) CD As the angle A changes, how do the other lengths in the diagram change? Is it possible for CD to have length 10? If so, what angle is needed? What about setting other lengths to 10? You can find the length of BD in one step by looking at the whole triangle, or two steps by considering the two small triangles. What do your answers tell you about the connection between sin, cos, and tan?