Hello, KevinVM20!

To answer your first question:

. . the unknown is __obviously__ the height of the tree.

I can look out my window and see the top of a tower.

On the map, I see that it is 2 miles away.

I read somewhere that the tower is 500 feet tall.

As I look at the tower, I see that the top leaves of a tree

sometimes get in the way of the top of the tower. **

The tree is 50 yards from where I sit.

How tall is the tree? ** I assume this means that the top of tree lines up

. . with the line-of-sight to the top of the tower.

We further assume that your eye and the base of the tower are at the same height.

Let $\displaystyle h$ = height of the tree (in feet).

Change all units to feet. Code:

*
* |
* |
* | 500
* |h |
* | |
* - - - - - * - - - - - *
: - 150 - :
: - - - 10,560 - - - - :

From the two similar right triangles, we have: .$\displaystyle \frac{h}{150} \:=\:\frac{500}{10,560} $

Therefore: .$\displaystyle h \;=\;\frac{75,000}{10,560} \;=\;\frac{625}{88} \;\approx\;7.1\text{ feet}$