SOLUTION: Please help with this word problem. 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? Ple

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Question 256426: Please help with this word problem. 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. For example where you get numbers. Thank you so much.
Found 2 solutions by ankor@dixie-net.com, solver91311:
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
You can put this solution on YOUR website!
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%2F120
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%2Fd
.6667 - d%2F600
d = 600%2F.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%2F600 = 120%2Fx
cross multiply
80x = 72000
x = 72000%2F80
x = ft from ant to building
then
900 - 120 = 720 ft from tree to building
:
Hope this helps

Answer by solver91311(24713) About Me  (Show Source):
You can put this solution on YOUR website!


Proportionality of Similar Triangles.

You have two similar triangles. The vertices of the smaller one are the ant, the bottom of the tree, and the top of the tree. The vertices of the larger one are the ant, the bottom of the building, and the top of the building.

We don't know how far it is from the bottom of the tree to the bottom of the building so let's call that .

The distance from the ant to the bottom of the tree is given as 120 ft. The distance from the ant to the bottom of the building is then .

So, to recap

Height of tree: 80

Height of building: 600

Ant to tree: 120

Ant to building:

Create the proportion:



Now all you need to do is cross-multiply and solve.

John