Apole that is 3.3 meters tall casts a shadow that is 1.69 meters long. at the same time, a nearby building casts a shadow that is 47.25 meters long. how tall is the building? round to the nearest meter.

92 meters

Step-by-step explanation:

This is a problem that can be solved by the concept of "similar triangles", where we have two right angle triangles that share also another common angle" the angle that the rays of the sun form with them (see attached image).

The smaller triangle is formed by the limiting rays of the sun, the pole, and its shadow: it has a height of 3.3 m (the length of the pole) and a base of 1.69 m (the pole's shadow).

The larger triangle is formed by the rays of the sun, the building and its shadow: it has a base of 47.25 m and an unknown height that we named as "x" (our unknown).

The ratio of the bases of such similar triangles must be in the same proportion as the ratio of their heights, so we can create a simple  equation that equals such ratios, and then solve for the unknown "x":

which we can round to the nearest meter as: 92 m