SOLUTION: I have a word problem. On a bright sunny day, two men are standing in an open plaza. The shorter man is wearing a hat that makes him appear to be the same height as the other man

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Question 194967: I have a word problem.
On a bright sunny day, two men are standing in an open plaza. The shorter man is wearing a hat that makes him appear to be the same height as the other man, who is not wearing a hat. The hat is made so that the top of it is 4 inches above the top of the wearer's head. When the shorter man takes off his hat, he casts a 51 inch shadow while the taller man casts a 54 inch shadow. How tall is each man?
Thank you
Answer by ankor@dixie-net.com(22740) About Me  (Show Source):
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On a bright sunny day, two men are standing in an open plaza. The shorter man is wearing a hat that makes him appear to be the same height as the other man, who is not wearing a hat. The hat is made so that the top of it is 4 inches above the top of the wearer's head. When the shorter man takes off his hat, he casts a 51 inch shadow while the taller man casts a 54 inch shadow. How tall is each man?
:
Let x = the height of the man without the hat
then
(x-4) = height of man with the hat
:
The triangles formed by the shadows and the men are similar (same angle to the sun)
therefore
%28%28x-4%29%29%2F51 = x%2F54
Cross multiply
54(x-4) = 51x
:
54x - 216 = 51x
:
54x - 51x = 216
:
3x = 216
x = 216%2F3
x = 72 inches, height of the hat-less man
then
68 inches is the height of the man with the hat