Dinesh and Yumiko are at the beach on a calm, sunny day, planning to wade into the gentle waves. They have found a relatively shallow area where the water depth increases gradually. On the shore, there's a wooden pier that stretches out over the water, providing an excellent vantage point for viewing the surroundings. The pier is about the height of an average adult and runs parallel to the shore. Both Dinesh and Yumiko have marked their respective heights on the pier with chalk before entering the water, and they both wade into the sea until the water reaches exactly up to their individual chalk marks when they stand straight.

While they are in the water, their friend Kaveh arrives. Kaveh stands on the pier and looks out toward his friends. From his perspective, part of Dinesh and Yumiko are obscured by the water's surface. He knows the height of the pier and has a clear view of where the chalk marks are in relation to his friends' current positions in the water. There is a tower further inland with a known height that is also visible from both the pier and the water.

In this scenario, considering the spatial positions of Dinesh and Yumiko in the water, their marked heights on the pier, the height of the onshore tower, and Kaveh's observations from the pier, answer the following spatial reasoning questions:

1. Based on the position of the chalk marks and the height of the water reaching those marks on Dinesh and Yumiko, what can Kaveh deduce about their heights in relation to each other and the tower without directly measuring them?
2. If Dinesh and Yumiko can both see the top of the tower from where they stand in the water, what does this indicate about the depth of the water where they are standing and each other's heights in relation to the tower?
Provide a short response.
1. When Kaveh looks from his position on the pier, he knows that the height of the pier is constant and, therefore, serves as a reference line for determining relative heights. Since Dinesh and Yumiko marked their heights on the pier, Kaveh can see that Dinesh's mark is lower than Yumiko's. Therefore, Kaveh can deduce that Dinesh is shorter than Yumiko when both are standing on solid ground. Now, considering the tower's height, if both marks are significantly lower than the tower's height and knowing that neither Dinesh nor Yumiko is taller than the tower, Kaveh can establish an approximate comparison of their heights with the tower's height. They are both shorter than the tower, and Dinesh is the shortest of the three.

2. Since both Dinesh and Yumiko can see the top of the tower while standing in water up to their respective marked heights, we can reason about the depth of the water. The fact that they can see the tower from their positions in the water suggests that their eye-levels are above the waterline. We also know that the water has not reached a point where it prevents them from seeing over the horizon to the tower's top. As the water depth where they are standing allows them to have a direct line of sight to the top of the tower, it confirms that the water depth does not exceed the height from their feet to their eyes. Hence, the water depth is less than the full height of either person.

If we also consider the curvature of the Earth and the height of the onshore tower, which would both be involved in more precise assessments of what can be seen from where, this reasoning simplifies the situation by not requiring precise measurements or mathematical calculations, relying instead on the general principle that as long as one's eyes are above the water level and there are no obstructions, they should be able to see the top of a taller structure. This situation assumes that the tower is close enough to be within the limit of their line of sight and not beyond the horizon.