math

We can use the property of similar triangles to solve this problem. The triangles formed by the poles and their shadows are similar, so the ratios of corresponding sides are equal. We can use this property to find which of the given options are plausible.

Let h1 and h2 be the heights of the tether ball pole and the flagpole, respectively, and let x1 and x2 be the lengths of their shadows. Then, we have:

h1 / x1 = h2 / x2

We know that h1 = 3 m and h2 = 6.8 m, so we can substitute these values:

3 / x1 = 6.8 / x2

Multiplying both sides by x1 x2, we get:

3x2 = 6.8x1

Simplifying, we get:

x1 = (3/6.8) x2

This means that the length of the tether ball pole's shadow is 3/6.8 times the length of the flagpole's shadow.

Now, we can check which of the given options satisfy this condition:

A) tether 1.35m, flag 3.4m
The ratio of their lengths is 1.35/3.4 = 0.397. This does not satisfy the condition.

B) tether 1.8m, flag 4.08m
The ratio of their lengths is 1.8/4.08= 0.441. This does not satisfy the condition.

C) tether 3.75m, flag 8.35m
The ratio of their lengths is 3.75/8.35 = 0.449. This satisfies the condition.

D) tether 0.6m, flag 1.36m
The ratio of their lengths is 0.6/1.36 = 0.441. This does not satisfy the condition.

E) tether 2m, flag 4.8m
The ratio of their lengths is 2/4.8 = 0.417. This does not satisfy the condition.

Therefore, the lengths of the shadows that could be plausible are C) tether 3.75m, flag 8.35m.