The Boy Mechanic, vol. 1, page 376
"Near the end of the season our boy announced the height of our tall maple tree to be 33 ft.
'Why, how do you know?' was the general question.
'Measured it.'
'How?'
'Foot rule and yardstick.'
'You didn't climb that tall tree?' his mother asked anxiously.
'No'm; I found the length of the shadow and measured that.'
'But the length of the shadow changes.'
'Yes'm; but twice a day the shadows are just as long as the things themselves. I've been trying it all summer. I drove a stick into the ground, and when its shadow was just as long as the stick I knew that the shadow of the tree would be just as long as the tree, and that's 33 ft.'"
Clever. It seems to me that with a little math you could calculate the height of the tree at any time of day. If the shadow of your stick is - for example - half the height of the stick, then the length of the shadow of the tree would be half the height of the tree. So you could multiply the length of the shadow by two (or whatever) to calculate the height of the tree.
“Let us urge forward our spirits, and make them approach the invisible world, and fix our mind upon immaterial things, till we clearly perceive that these are no dreams; nay, that all things are dreams and shadows besides them.”
–Henry Scougal, The Life of God in the Soul of Man