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?
To determine the length of the man's shadow, we can use the concept of similar triangles.
First, we need to establish the relationship between the height of the man and the height of the light post. The man's height is given as 5'6", which we can convert to feet only. Since there are 12 inches in a foot, the man's height can be written as 5 + 6/12 = 5.5 feet.
Now, we can set up the proportion between the height of the man and the height of the light post:
(man's height) / (light post's height) = (man's shadow length) / (distance from the base of the light post)
Plugging in the given values, we have:
5.5 feet / 18 feet = (man's shadow length) / 5 feet
To find the man's shadow length, we can solve for this variable:
(man's shadow length) = (5.5 feet / 18 feet) * 5 feet
Calculating this expression, we get:
(man's shadow length) ≈ 1.53 feet
Therefore, when the man is 5 feet from the base of the light post, his shadow will be approximately 1.53 feet long.