A flagpole casts a 32-ft shadow. A boy who is 6 feet tall is standing near the flagpole casting a 16-ft shadow. They form similar triangles. How tall is the flagpole?
Use a proportion, cross multiply, and solve for x.
6/16 = x/32
12ft
Well, it seems like the flagpole and the boy are both casting a shadow, having a little competition there, huh? Now, since they form similar triangles, we can use some math magic to find out the height of the flagpole.
Let's call the height of the flagpole "x." Now, we know that the height of the boy is 6 feet and the length of his shadow is 16 feet. We also know that the length of the flagpole's shadow is 32 feet.
To find the ratio of the height of the flagpole to the height of the boy, we can use the ratio of their shadows. So, we have:
x/6 = 32/16
Now, let's simplify that equation a bit:
x/6 = 2
If we cross multiply, we get:
x = 12
So, the height of the flagpole is 12 feet!
Seems like the flagpole is just trying to overshadow the boy, but the boy won this one!
To find the height of the flagpole, we can set up a proportion using the similar triangles formed by the flagpole and the boy:
Height of flagpole / Length of flagpole's shadow = Height of boy / Length of boy's shadow
Let's use the given values:
Height of boy = 6 ft
Length of boy's shadow = 16 ft
Plugging in these values into the proportion:
Height of flagpole / 32 ft = 6 ft / 16 ft
We can simplify the proportion:
Height of flagpole / 32 ft = 3 / 8
To solve for the height of the flagpole, we cross-multiply:
(Height of flagpole) * 8 = 32 ft * 3
Height of flagpole = (32 ft * 3) / 8
Height of flagpole = 12 ft
Therefore, the height of the flagpole is 12 feet.
To find the height of the flagpole, we can use the concept of similar triangles.
Similar triangles have proportional sides. In this case, the boy's height (6 feet) corresponds to his shadow length (16 feet), and the height of the flagpole corresponds to its shadow length. Let's call the height of the flagpole "x."
We can set up a proportion:
(Boy's height)/(Boy's shadow) = (Flagpole's height)/(Flagpole's shadow)
Substituting the given values:
6/16 = x/32
To solve for x, we cross-multiply:
6 * 32 = 16 * x
192 = 16x
Divide both sides by 16:
x = 192/16
x = 12
Therefore, the flagpole is 12 feet tall.