To determine the height of the building using similar triangles, we can set up a ratio using the heights and the lengths of the shadows of the pole and the building.
Let \( h \) be the height of the building. The height of the pole is 10 ft, and the shadows are as follows:
- Shadow of the pole: 5.75 ft
- Shadow of the building: 179 ft
Since the poles and buildings cast shadows due to the same light source, the triangles formed by their heights and shadows are similar. Therefore, we can set up the following proportion:
\[ \frac{\text{Height of the pole}}{\text{Length of the shadow of the pole}} = \frac{\text{Height of the building}}{\text{Length of the shadow of the building}} \]
Substituting in the known values:
\[ \frac{10 \text{ ft}}{5.75 \text{ ft}} = \frac{h}{179 \text{ ft}} \]
Now we can cross-multiply to solve for \( h \):
\[ 10 \text{ ft} \times 179 \text{ ft} = 5.75 \text{ ft} \times h \]
Calculating the left side:
\[ 1790 \text{ ft}^2 = 5.75 \text{ ft} \times h \]
Now, divide both sides by 5.75 ft to isolate \( h \):
\[ h = \frac{1790 \text{ ft}^2}{5.75 \text{ ft}} \approx 311.3043 \text{ ft} \]
Rounding this to the nearest foot gives:
\[ h \approx 311 \text{ ft} \]
Thus, the height of the building is approximately \(\boxed{311}\) feet.