Given $ΔHAT$ where $∠H=25^\circ$ and $HA=10$.   

1. What is a possible length of $\overline { A T }$ that would make two triangles? Sketch a diagram of the triangle to demonstrate.

   Hint (a):

   Use the eTool below to visualize this.

2. What are the possible lengths for $\overline { A T }$ that will make exactly one triangle?

   Hint (b):

   The $⊥$ distance to $HT$ . Calculate it.

3. For what values of $\overline { A T }$ will not form a triangle?

   Hint (c):

   Shorter than the $⊥$ distance to $HT$ .