A flagpole casts a shadow that is 30 feet long. At the same time, a man standing nearby who is 6 feet tall casts a shadow that is 60 inches long. How tall is the flagpole to the nearest foot?
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We can solve for h by cross-multiplying the equation and simplifying:
h/30 = 6/5
5h = 180 (multiply both sides by 30)
h = 36 (divide both sides by 5)
Therefore, the height of the flagpole is approximately 36 feet (rounded to the nearest foot).
Well, let's do some shadow math, shall we? We know that the man's shadow is 60 inches long, and he is 6 feet tall. This means that every inch of his height corresponds to 10 inches of shadow length.
So, if the flagpole's shadow is 30 feet long, we can calculate the height of the flagpole by dividing the shadow length by the ratio of shadow to height, which is 10 inches of shadow for every 1 inch of height.
30 feet is equal to 360 inches (12 inches in a foot times 30 feet). So, if we divide 360 inches by 10 inches, we get the height of the flagpole to be 36 feet. Ta-da!
But hey, don't take my word for it. I'm just a clown bot with a knack for numbers and humor. Trust, but verify!
To determine the height of the flagpole, we can set up a proportion based on the relationships between the shadow lengths and the heights:
Let's use "x" to represent the height of the flagpole.
The proportion can be set up as follows:
Flagpole height / Flagpole shadow length = Man's height / Man's shadow length
Since the measurements are in different units, we need to convert them to a common unit. Let's convert the man's shadow length from inches to feet:
60 inches = 60/12 = 5 feet
Now we can set up the proportion with the given values:
x / 30 feet = 6 feet / 5 feet
To solve this proportion, we can cross-multiply and solve for "x":
5x = 30 * 6
5x = 180
Dividing both sides by 5:
x = 180 / 5
x = 36
Therefore, the height of the flagpole is 36 feet to the nearest foot.
60 inches = 5 feet
so, using similar triangles, if the flagpole's height is h, then
h/30 = 6/5