A 25 foot tall flagpole cast =s a 20 foot shadow. If a man with a height of 6 feet stands nearby, what will be the lenghth of this shadow?

the ratio of shadow length to height is the same for pole and man, so

x/6 = 20/25

now just solve for x

Or, you could just say that the heights and shadows have the same ratio, so

x/20 = 6/25

25/20 = 6/x

25x = 120
x = 120/25 = 24/5 or 4.8 ft

Well, if a 25-foot flagpole casts a 20-foot shadow, and the man is only 6 feet tall, I have a feeling that his shadow would be pretty disappointed with its length. It would probably want to be longer, but alas, it can only dream. So to answer your question, the length of the man's shadow will depend on how much it longs to be as long as the flagpole's shadow.

To find the length of the shadow, we can compare the ratios of the flagpole's height and its shadow to the man's height and the unknown shadow.

The ratio of the flagpole's height to its shadow length is 25:20. We can simplify this ratio by dividing both the height and shadow by 5: 5:4.

Since the height ratio is 5:4, we can apply it to the man's height of 6 feet.

(6 feet / 5) * 4 = 4.8 feet.

Therefore, the length of the shadow of the man will be approximately 4.8 feet.

To determine the length of the man's shadow, we can use the concept of similar triangles. Since the ratio of the flagpole's height to its shadow length is the same as the ratio of the man's height to his shadow length, we can set up a proportion to solve for the length of the man's shadow.

Let's denote the length of the man's shadow as "x". The given measurements are as follows:
Flagpole height = 25 feet
Flagpole shadow length = 20 feet
Man's height = 6 feet

We can set up the proportion as follows:

Flagpole height / Flagpole shadow length = Man's height / Man's shadow length

Substituting in the given values:
25 / 20 = 6 / x

To solve for x, we can cross multiply:
25 * x = 20 * 6

Simplifying further:
25x = 120

Dividing both sides by 25:
x = 120 / 25

Calculating the value:
x ≈ 4.8 feet

Therefore, the length of the man's shadow will be approximately 4.8 feet.