To find the height of the building, we can use the concept of similar triangles. The ratio of the height of the pole to the length of its shadow will be the same as the ratio of the height of the building to the length of its shadow.
Let \( h \) be the height of the building. According to the problem, we have:
- Height of the pole = 2.9 m
- Length of the pole's shadow = 1.24 m
- Length of the building's shadow = 38.5 m
We can set up the following proportion:
\[ \frac{\text{Height of the pole}}{\text{Length of the pole's shadow}} = \frac{\text{Height of the building}}{\text{Length of the building's shadow}} \]
Substituting the values we know:
\[ \frac{2.9}{1.24} = \frac{h}{38.5} \]
Now we will cross-multiply to solve for \( h \):
\[ 2.9 \times 38.5 = 1.24 \times h \]
Calculating the left side:
\[ 2.9 \times 38.5 = 111.65 \]
So, we have:
\[ 111.65 = 1.24h \]
Now, divide both sides by 1.24 to find \( h \):
\[ h = \frac{111.65}{1.24} \approx 90.0 \]
Thus, the height of the building is approximately 90 m. Therefore, rounded to the nearest meter, the height of the building is:
\[ \boxed{90} \]