SOLUTION: If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10 inches tall casts a shadow of 5 feet, then the height of the tree is?

Algebra ->  Triangles -> SOLUTION: If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10 inches tall casts a shadow of 5 feet, then the height of the tree is?      Log On


   

Question 1188704: If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10 inches tall casts a shadow of 5 feet, then the height of the tree is?
Found 2 solutions by ikleyn, Shin123:
Answer by ikleyn(52810) About Me  (Show Source):
You can put this solution on YOUR website!
.
If a tree casts a shadow 12 feet long and at the same time a person who is 5 feet 10 inches tall casts
a shadow of 5 feet, then the height of the tree is?
~~~~~~~~~~~~~~


This exercise is for those amateurs who love convert inches to feet and vise versa. 

5 feet 10 inches = 5*12 + 10 inches = 60 + 10 inches = 70 inches.


To solve the problem, write a proportion


    shadow%2Fheight = 12%2Fx = 60%2F70.


From the proportion, find  x = %2812%2A70%29%2F60= %2812%2A7%29%2F6 = 2*7 = 14 feet.    ANSWER

Solved.



Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
The ratio from an object's height to its shadow is constant regardless of the object. Therefore, we have that x%2F12=5%265%2F6%2F5, where x is the height of the tree. Multiplying both sides by 12, we get feet.