Agate post is 7 feet tall. the gate posts cast a shadow that is 10 feet long. a nearby flag pole casts a shadow that is 30 feet long. how tall is the flag pole? (hint: use the properties of similar triangles.) a. 21 ft b. 70 ft c. 210 ft d. 300 ft

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.

40 & 50 in the right corner are the complementary angles as when placed in a sum (added together) they make 90°