SOLUTION: Use similar triangle to solve: A person who is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86-foot shadow. The person's shadow is 6 feet in lengt

Algebra ->  Triangles -> SOLUTION: Use similar triangle to solve: A person who is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86-foot shadow. The person's shadow is 6 feet in lengt      Log On


   

Question 1153480: Use similar triangle to solve:
A person who is 5 feet tall is standing 80 feet from the base of a tree and the tree casts an 86-foot shadow. The person's shadow is 6 feet in length. What is the tree's height?
Please show steps to solve.
Thank you in advance,
SYL
Found 2 solutions by greenestamps, Edwin McCravy:
Answer by greenestamps(13198) About Me  (Show Source):
You can put this solution on YOUR website!


With the problem presented as it is, the person's distance from the tree is irrelevant.

Assuming the tree and the person are standing perpendicular to the ground, the triangles formed by the tree and the person, their shadows, and the rays of light that produce the shadows are similar right triangles.

According to corresponding parts of similar triangles,
tree's height     person's height
-------------  =  ---------------
tree's shadow     person's shadow

x%2F86+=+5%2F6

x+=+%285%2F6%29%2A86+=+430%2F6+=+215%2F3 or 71 2/3 feet

Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
Use similar triangle to solve:
A person who is 5 feet tall is standing 80 feet from the base of a tree and the
tree casts an 86-foot shadow. The person's shadow is 6 feet in length. What is
the tree's height?
Please show steps to solve.
Thank you in advance,
SYL
This has some unnecessary information.  It was put in to see if you would try to
use it in solving the problem.  But it doesn't matter whether you're 80 feet or
100 feet or 73 feet or 29 feet from the base of a tree!  The lengths of the
shadows of the man and the tree aren't going to change because he moves nearer
to or farther from the tree!  So "80 feet" is unnecessary information and must
be ignored.   

 

"IS TO" means "OVER" and "AS" means "EQUALS".

So, 



So,



So,



So we cross multiply:





We divide both sides by 6



We reduce the fraction by dividing top and bottom by 2



Change to a mixed number:



Edwin