SOLUTION: I have a solution of 3.1875 meters for this problem but it is in error. (I calculated height/distance from lamppost to the man as 8/15; calculated height/distance from man to end

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Question 155516: I have a solution of 3.1875 meters for this problem but it is in error. (I calculated height/distance from lamppost to the man as 8/15; calculated height/distance from man to end of shadow as 1.7/x). I appreciate your help!
A man is walking away from a lamppost with a light source 8 meters above the ground. The man is 1.7 meters tall. How long is the man's shadow when he is 15 meters from the lamppost?
Thanks, Linda
Found 3 solutions by oscargut, stanbon, Earlsdon:
Answer by oscargut(2103) About Me  (Show Source):
You can put this solution on YOUR website!
%288%2F%2815%2Bx%29%29=%281.7%2Fx%29
then
8x=1.7%2815%2Bx%29
8x=25.5%2B1.7x
6.3x=25.5
x=25.5%2F6.3=4.047619
Answer: 4.0477 m (aprox)

Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
A man is walking away from a lamppost with a light source 8 meters above the ground. The man is 1.7 meters tall. How long is the man's shadow when he is 15 meters from the lamppost?
------------------------
Draw the picture.
The lamppost is the height of the larger triangle;
The man is height of the smaller SIMILAR triangle.
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Let the base of the larger triangle be x.
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EQUATION:
8 meters/ 1.7 meters = x/x-15
8(x-15) = 1.7x
8x - 120 = 1.7x
6.3x = 120
x = 19.048
----------------
Man's shadow = 19.048-15 = 4.048 meters
=========================================
Cheers,
Stan H.

Answer by Earlsdon(6294) About Me  (Show Source):
You can put this solution on YOUR website!
You can use the priniples of similar triangles here.
Let the length of the man's shadow be x meters.
The 8-meter lampost is the height of the first right triangle while the 1.7-meter man is the height of the second right triangle.
The base of the first triangle is 15+x meters while the base of the second right triangle is x meters, which is what we are trying to find.
The rule is "Corresponding sides of similar triangles are proportional"
So we can write the proportion:
8%2F%28x%2B15%29+=+1.7%2Fx Do you see this? Now we solve for x, the length of the man's shadow by cross-multiplying.
8x+=+1.7%28x%2B15%29 Simplifying, we get:
8x+=+1.7x%2B25.5 Subtract 1.7x from both sides.
6.3x+=+25.5 Divide both sides by 6.3
x+=+4.047
The length of the man's shadow is 4.047 meters (approximately).