Final answer:
Using similar triangles and setting up a proportion, it is calculated that the length of the person's shadow is approximately 3.2 feet when they are standing 10 feet away from a 25-foot tall lamppost.
Step-by-step explanation:
To find the length of the person's shadow when they are 10 feet away from a lamppost, we'll use similar triangles. We know the person is 6 feet tall and the lamppost is 25 feet tall. If the person walks 10 feet away from the base of the lamppost, we can set up a proportion: (height of the person)/(length of the person's shadow) = (height of the lamppost)/(distance from the lamp post + length of shadow).
So, it will look something like this:
6 / s = 25 / (10 + s)
Multiply both sides by (10 + s) to solve for the shadow length (s):
6(10 + s) = 25s
60 + 6s = 25s
19s = 60
s = 60 / 19
s ≈ 3.2 feet
Therefore, the length of the person's shadow, rounded to the nearest tenth of a foot, is approximately 3.2 feet.
To find the length of the person's shadow when they are 10 feet from the lamppost, we can use similar triangles. The height of the lamppost is 25 feet, and the person's height is 6 feet. Let x be the length of the person's shadow. We can set up the proportion:
6 / x = 25 / (x + 10)
Cross-multiplying and solving for x, we get:
x = (6 * (x + 10)) / 25
Combining like terms:
25x = 6x + 60
19x = 60
x ≈ 3.2 feet