Final answer:
By setting up a proportion based on the similar triangles formed by the tower and its shadow and the pole and its shadow, we can determine that the height of the tower is 48 feet.
Step-by-step explanation:
The problem describes two similar triangles: one formed by the tower and its shadow, and the other formed by the pole and its shadow. This is because both the tower and the pole cast shadows due to sunlight coming at the same angle. We can set up a proportion to find the height of the tower because similar triangles have corresponding sides that are proportional. Let x be the height of the tower. The ratio of the height of the pole to its shadow length is equal to the ratio of the height of the tower to its shadow length.
Using the proportion, we have 6 feet (height of pole) / 8 feet (length of pole's shadow) = x (height of tower) / 64 feet (length of tower's shadow).
This can be simplified to:
∃/4 = x/64
By cross-multiplying, we get:
6 * 64 = 8x
384 = 8x
Divide both sides by 8 to solve for x:
x = 48
Therefore, the height of the tower is 48 feet.