A50-foot flagpole is at the entrance of a building that is 300 feet tall. if the length of the flagpoles shadow is 30 feet at a certain time of day, how long is the building's shadow at that time?

The two triangles are similar because the angle of the sun is the same at the same time of day and (hopefully) both the flagpole and the building are upright making a right triangle with the ground. So all three angles of each triangle is equal to a corresponding angle of the other triangle. Since they are similar the sides are proportional to the corresponding sides in the other triangle, so height of flagpole / length of flagpole's shadow = height of building/ length of building's shadow. 50'/30' = 300'/x (5/3) x = 300' 5x = 900' x= 180'. Length of building shadow is 180 feet