Final answer:
The height of the building is 10 meters as it forms a right-angled triangle with a 45-degree angle of elevation and a 10-meter base.
Step-by-step explanation:
The angle of elevation to the top of a story building from a point on the ground 10 m away is 45 degrees. To find the height of the building, we use the concept of a right-angled triangle. Given the angle of elevation and the distance from the observer to the building's base, we can say that the height of the building is equivalent to the distance on the ground, because in a 45-degree right-angled triangle, the adjacent side and the opposite side are of equal length. Thus, if the angle of elevation is 45 degrees and the distance is 10 m, the height of the building would also be 10 m.