Posted by Sasuke on Wednesday, August 1, 2012 at 11:39am.
If you draw a diagram, you will see that you cannot compute the height of the tree without knowing how far apart are the tower and the tree.
The observer is 80-6.5=73.5 above the base of the tower and the base of the tree.
An angle of depression to the base of the tree of 72-20-00 means that the distance between the tower and the tree is D=73.5/tan(72-20-00)
the difference between the top of the tree and the observer is therefore
h=D sin(12-40)
The height of the tree, H, is then
H=73.5+D sin(12-40)
=73.5 + 73.5 sin(12-40-00)/tan(72-20-00)
=73.5(1+sin(12-40-00)/tan(72-20-00))
=78.6 ft
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