Here's a plan of the view on the ground:

Let (T'denotes the base of the tower, so I'm using x to denote the horizontal distance fromOto the base of the tower,notthe inclined distance to the top of the tower). Then . From the picture, . Therefore , and so .

Next, , so . But by Pythagoras (see the above diagram), Thus , and I guess you can take it from there to get the formula for tan^2(θ). Once you have that, the remaining two parts of the question are easy.