Final answer:
Using similar triangles, the building's height is calculated as 64 meters when the height of a pole and the respective shadows of the pole and the building are known.
Step-by-step explanation:
A pole that is 2.7 meters (M) tall casts a shadow that is 1.68 meters (M) long, and at the same time, a nearby building casts a shadow that is 39.75 meters (M) long. The height of the building can be calculated using similar triangles, where the ratio of the height of the pole to its shadow length is the same as the ratio of the height of the building to its shadow length:
Height of pole / Shadow of pole = Height of building / Shadow of building
2.7 M / 1.68 M = Height of building / 39.75 M
Now we solve for the height of the building:
Height of building = (2.7 M / 1.68 M) × 39.75 M
Height of building = (1.607143) × 39.75 M
Height of building = 63.934524 M
When rounded to the nearest meter, the height of the building is 64 meters.