A 5'6" person is standing near a light post that is 18' above the ground. How long is the man's shadow when he is 5' from the base of the light post?
using similar triangles, if the length of the shadow is s,
5.5/18 = s/(5+s)
s = 2.2 ft
To find the length of the man's shadow, we can use similar triangles. Let's define a few variables:
Let h be the height of the light post (18').
Let p be the height of the person (5').
Let d be the distance between the person and the base of the light post (5').
We can set up a proportion between the corresponding sides of the two similar triangles formed:
(Length of the shadow)/(h + p) = d/h
Using this proportion, we can solve for the length of the shadow:
Length of the shadow = (d * (h + p))/h
Substituting the given values:
Length of the shadow = (5' * (18' + 5'))/18'
To calculate this, we need to convert the measurements into a common unit. Let's convert feet to inches:
Length of the shadow = (5 * (18 + 5))/18
Now, we can solve the equation:
Length of the shadow = (5 * 23)/18
= 115/18
Therefore, the length of the man's shadow, when he is 5' from the base of the light post, is approximately 6.39 feet.