To solve for the height of the tower, we can use similar triangles. The ratio of the height of an object to the length of its shadow is the same for both the pole and the tower.
Let \( h \) be the height of the tower. According to the problem:
- The height of the pole is 7 ft.
- The length of the pole's shadow is 6.75 ft.
- The length of the tower's shadow is 187 ft.
Using the proportion, we have:
\[ \frac{\text{Height of Pole}}{\text{Shadow of Pole}} = \frac{\text{Height of Tower}}{\text{Shadow of Tower}} \]
Substituting the known values:
\[ \frac{7 \text{ ft}}{6.75 \text{ ft}} = \frac{h}{187 \text{ ft}} \]
Now, we can cross-multiply to solve for \( h \):
\[ 7 \text{ ft} \times 187 \text{ ft} = 6.75 \text{ ft} \times h \]
Calculating \( 7 \times 187 \):
\[ 7 \times 187 = 1309 \]
Thus, we have:
\[ 1309 = 6.75h \]
Now, divide both sides by 6.75 to find \( h \):
\[ h = \frac{1309}{6.75} \]
Calculating \( \frac{1309}{6.75} \):
\[ h \approx 193.15 \]
Rounding to the nearest foot, we find:
\[ h \approx 193 \]
Thus, the height of the tower is \( \boxed{193} \) ft.