When the sun casts shadows on different objects at the same time it creates similar right triangles. Examines the similar triangles below:
How tall is the tree?
What is the Scale Factor from the tree to the person?
What is the Scale Factor from the person to the tree?
The height, h, is given by :
6/9 = h/ 24 cross-multiply
24*6 = 9h
144 = 9h divide both sides by 9
16 = h
The scale factor from the height of the tree to the height of the person = 6/16 = 3/8
The scale factor from the height of the person to the height of the tree = 16/6 = 8/3