To answer your first question:
. . the unknown is obviously the height of the tree.
** I assume this means that the top of tree lines up 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?
. . 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 = height of the tree (in feet).
Change all units to feet.
* | 500
* |h |
* | |
* - - - - - * - - - - - *
: - 150 - :
: - - - 10,560 - - - - :
From the two similar right triangles, we have: .