Final answer:
To determine the height of the tower, we set up a proportion based on the lengths of shadows cast by the pole and the tower, which are in similar triangles. After cross-multiplying and dividing, we find that the tower's height is 42 meters.
Step-by-step explanation:
The question involves using similarity in triangles to find the height of the tower. The vertical pole and the tower create similar triangles with their respective shadows. Since the pole is 6 meters high and casts a 4-meter shadow, and the tower casts a shadow of 28 meters, we can set up a proportion to find the height of the tower.
Using the fact that the ratios of corresponding sides in similar figures are equal, we set up the proportion as follows:
Height of Pole / Length of Pole's Shadow
= Height of Tower /Length of Tower's Shadow
So, 6m / 4m = Height of Tower / 28m
Cross multiply to solve for the Height of Tower:
6m * 28m = 4m * Height of Tower
168m2 = 4m * Height of Tower
Divide both sides by 4m to get the Height of Tower:
Height of Tower = 168m2 / 4m
Height of Tower = 42m
Therefore, the height of the tower is 42 meters.