SOLUTION: A spotlight is placed 2 feet from a 1-foot tall vase. A shadow 5 feet tall is cast on a wall. Find the distance of the vase from the wall.

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Question 1136112: A spotlight is placed 2 feet from a 1-foot tall vase. A shadow 5 feet tall is cast on a wall. Find the distance of the vase from the wall.
Found 2 solutions by josgarithmetic, ikleyn:
Answer by josgarithmetic(39620) About Me  (Show Source):
You can put this solution on YOUR website!
simple pythagorean theorem formula application

Answer by ikleyn(52812) About Me  (Show Source):
You can put this solution on YOUR website!
.
It is about proportions . . . 


You have two similar (right-angled) triangles.


The legs of the smaller triangle are 2 ft and 1 ft, where 1 ft is the height of the vase.


The legs of the greater triangle are (2+x) ft and 5 ft.


The unknown x is the distance of the vase from the wall.


The proportion (from the triangles similarity) is


    1%2F2 = 5%2F%282%2Bx%29.


From the proportion


    2+x = 2*5 = 10  =============>  x = 10-2 = 8.


ANSWER.  The distance from the vase to the wall is 8 ft.

Solved.

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Ignore the post by  @josgarithmetic,  since it is   t o t a l l y     I R R E L E V A N T.



When you obtain something from @josgarithmetic,  be very careful,  because,  AS  A  RULE, 

    1)  he can not read a problem correctly;

    2)  he can not interpret correctly what he reads;

    3)  he can not solve a problem correctly;

    4)  he can not present a solution correctly.


He only can create some  "white noise"  and  "dirty wrong solutions"  in this forum,  that never are useful.