This problem involves using similar triangles because both the tree and the vertical rod are casting shadows at the same time under the same sunlight.

We can set up a proportion using the heights and shadow lengths:

$\frac{\text{Height of the tree}}{\text{Shadow of the tree}} = \frac{\text{Height of the rod}}{\text{Shadow of the rod}}$

Let $h$ be the height of the tree, which we are trying to find. Then, the equation is:

$\frac{h}{14} = \frac{28}{8}$

Now, solve for $h$:

$h = \frac{28}{8} \times 14$

Let's calculate the value of $h$.

The height of the tree is 49 feet.

Would you like more details or have any further questions?

Here are 5 related questions you can try:

1. If the tree's shadow were 20 feet long, how tall would the tree be under the same conditions?
2. If a building casts a shadow 35 feet long, and a 10-foot pole casts a 5-foot shadow at the same time, how tall is the building?
3. What would be the height of a flagpole if it casts a 12-foot shadow, and a 6-foot pole casts a 4-foot shadow at the same time?
4. If the sun's angle changes, causing a tree's shadow to lengthen by 10 feet, how does this affect the height-to-shadow ratio?
5. How can you use trigonometry to determine the height of a tree if the angle of elevation of the sun is known?

Tip: When two objects cast shadows under the same sunlight, their height-to-shadow ratios remain the same due to similar triangles.