So we have two similar triangles; with the given gate post and the flag pole. We are trying to find X, the height of the flag pole.
Since these triangles are similar, we can put the side lengths of each triangle in a proportion equal to each other.
The ratio of the height of the gate post over its shadow is 7 / 10. And the ratio of the height of the flag pole over its shadow is x / 30.
We have to cross multiply to figure out x alone. I’ll attach a picture so it’s a bit easier to see.
So we are left with 30 • 7 = 10x.
30 • 7 = 210.
210 = 10x
With your knowledge of basic algebra, you should know what to do. You divide 210 / 10, to get 21 ft. Which is your answer. Voila.