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

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)   (Show Source): You can put this solution on YOUR website!

then

Answer: 4.0477 m (aprox)

Answer by stanbon(75887)   (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.
----------------
Let the base of the larger triangle be x.
-------------------
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)   (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:
Do you see this? Now we solve for x, the length of the man's shadow by cross-multiplying.
Simplifying, we get:
Subtract 1.7x from both sides.
Divide both sides by 6.3

The length of the man's shadow is 4.047 meters (approximately).
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