Question 256426
 An ant is 120 ft. from an 80 ft. tall tree whose top is the visual line of a 600 ft. tall building.
 How far is the tree from the building? Please explain every step.
:
Find the angle of sight from the ant to the tree
Use the tangent of the angle(A): Side opposite (80ft) over Side adjacent (120ft)
:
tan(A) = {{{80/120}}}
tan(A) = .6667
A = 33.69 degrees
:
Use the tan of the same angle to find the dist (d) from the ant to the building
Side opposite (600) over side adjacent (d)
tan(33.69) = {{{600/d}}}
.6667 - {{{d/600}}}
d = {{{600/.667}}}
d =  900 ft from the Ant to the building
therefore
900 - 120 = 780 ft from the tree to the building
:
:
After seeing the problem, I read it again and see I made a mistake, I put 600 as the line of sight distance instead of the building height,  Sorry. Obviously your teacher did it a different way.
:
Using a simpler method, ratios of corresponding sides:
tree height to building height is to ant/tree dist to ant/building dist (x)
{{{80/600}}} = {{{120/x}}}
cross multiply
80x = 72000
x = {{{72000/80}}}
x = ft from ant to building
then
900 - 120 = 720 ft from tree to building
:
Hope this helps