geometrY
posted by shannon .
See the last picture at the bottom of this web page (for a pic of this exact problem).
Using ratios,
Tree height = T
15/66 = 6.33/T
15T = 512.73
T = 34.182
T = 34.182 when getting this answer from my question: to estimate the height of a tree, Dave stands in the shadow of the tree so that his shadow and the tree's shadow end at the same point. Dave is 6 feet 4 inches tall and his shadow is 15 feet long. If he is standing 66 feet away from the tree, what is the height of this tree? why was it 6.33/T (where did that come from?)

Shannon, I'm very sorry. The setup is wrong (1st line), but the rest is correct. I have no idea where I got that first line.
http://member.tripod.com/~BDaugherty/GCSEMaths/shapes.html
In the picture, the ratio is
T/30 = 2/3
3T = 60
T = 20
Your problem, with the corrected first line is
Using ratios,
Tree height = T
T/81 = 6.33/15
15T = 512.73
T = 34.182