Final answer:
Using a proportional relationship derived from similar triangles, the height of the tower is calculated as approximately 82 meters tall when rounded to the nearest meter.
Step-by-step explanation:
To find the height of the tower, we can use similarity in right triangles. The pole and tower, along with their shadows, form two right triangles that are similar to each other. This means the ratios of the heights to the shadows of the pole and tower are equal:
Pole's height / Pole's shadow = Tower's height / Tower's shadow
Given the pole's height is 3.5m, and its shadow is 1.55m and the tower's shadow is 36.25m, we can set up the proportion:
3.5m / 1.55m = Tower's height / 36.25m
By cross-multiplying, we solve for the Tower's height:
3.5m * 36.25m = Tower's height * 1.55m
126.875m² = Tower's height * 1.55m
The tower's height is then:
Tower's height = 126.875m² / 1.55m
Tower's height = ≈82.5m
After rounding the tower's height to the nearest meter, we find that the tower is approximately 82 meters tall