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.Com
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)   (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



or 71 2/3 feet


Answer by Edwin McCravy(20054)   (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

RELATED QUESTIONS

Use similar triangles to solve. A person who its 5 feet tall is standing 143 feet from... (answered by KMST)
A person who is 5 feet tall is standing 80 feet from the base of a tree. The tree casts... (answered by rfer)
If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10... (answered by ikleyn,Shin123)
A 5 foot tall boy casts an 11 foot chadow. The boy is standing 30 feet from a tree. How... (answered by Alan3354)
Use the diagram to solve for the given segments below. You can assume that the tree,... (answered by josgarithmetic,greenestamps)
A tree casts a shadow 10 ft long. A boy standing next to the tree casts a shadow 2.5 ft... (answered by malglu)
I am not sure how to handle this problem I hope you can help me Cassidy is standing... (answered by edjones)
A 5-foot tall woman casts a shadow of 6 feet. At the same time, a tree casts a shadow of... (answered by Boreal)
a PERSON WHO IS 6 FEET TALL CASTS A SHADOW 32 FEET LONG BETWEEN (N) AND (G), THE DISTANCE (answered by Alan3354)