A flagpole casts a shadow 10 ft long. If a man 6 ft tall casts a shadow 4 ft long at the sme time of day, how tall is the flagpole?

solve for h, the height of the flagpole

h/10 = 6/4

15 ft

To find the height of the flagpole, we can set up a proportion using the similar triangles formed by the flagpole and the man.

Let's denote the height of the flagpole as "x" and its shadow length as "10 ft".
Similarly, we have the height of the man as "6 ft" and his shadow length as "4 ft".

Using the property of similar triangles, we can set up the following proportion:

(man's height) / (man's shadow length) = (flagpole's height) / (flagpole's shadow length)

6 ft / 4 ft = x / 10 ft

Simplifying the proportion:

1.5 = x / 10

Now, we can solve for "x" by cross-multiplying:

1.5 * 10 = x

15 = x

Therefore, the height of the flagpole is 15 ft.

To find the height of the flagpole, we can set up a proportion using similar triangles formed by the flagpole and the man's height and their respective shadows.

Let's assume the height of the flagpole is 'h'.

The proportion can be set up as follows:

(height of the flagpole)/(length of flagpole's shadow) = (height of the man)/(length of the man's shadow)

h/10 = 6/4

Now, we can solve the proportion by cross-multiplication:

4h = 6 * 10

4h = 60

Dividing both sides of the equation by 4:

h = 60/4

h = 15

Therefore, the height of the flagpole is 15 feet.