Final answer:
Using the concept of similar triangles, we find that a pole with a height of 10 meters 50 cm will cast a shadow that is 6 meters long at the same time of day as a 5 meter 60 cm tall pole casting a 3 meter 20 cm shadow.
Step-by-step explanation:
The question involves finding the length of the shadow cast by a different pole given the shadow length of a similar pole and its height. This can be solved using similar triangles as the pole and its shadow create a right triangle with the ground. The length of the shadow is directly proportional to the height of the pole when the angle of the sunlight is constant. Therefore, if we have a 5 meter 60 cm (5.6 m) tall pole casting a 3 meter 20 cm (3.2 m) long shadow, we can set up a proportion to find the shadow length of a 10 meter 50 cm (10.5 m) tall pole.
Let's denote the unknown shadow length as x. The proportion based on similar triangles is as follows:
- Pole height 1 / Shadow length 1 = Pole height 2 / Shadow length 2
- 5.6 m / 3.2 m = 10.5 m / x
- x = (10.5 m * 3.2 m) / 5.6 m
- x = 6 m
Therefore, at the same time of day, a pole with a height of 10 meters 50 cm will cast a shadow that is 6 meters long.