Some Native Americans had a very interesting way of doing this. To see how high a tree was, they would find a spot where, looking under their legs (as shown), they could just see the top of the tree. The distance from such a spot to the base of the tree was approximately the height of the tree.
Why does this work? The reason is quite simple. For a normal, healthy adult, the angle formed by looking under one's legs is approximately 45o. Hence, the distance to the tree must be around the same as the height of the tree.