This problem can be solved using the concept of similar triangles. The setup forms two similar right triangles: one formed by Travis and his shadow, and the other formed by the tree and its shadow.

Step-by-Step Solution

1. Define the Variables:

   • Height of Travis: $h_t = 1.55 \, \text{m}$
   • Length of Travis's shadow: $s_t = 16.8 \, \text{m}$
   • Length of the tree's shadow: $s_{tree} = 21.15 \, \text{m}$
   • Height of the tree: $h_{tree} \, \text{(to be determined)}$

2. Key Similarity Property: Since the triangles are similar: $\frac{h_t}{s_t} = \frac{h_{tree}}{s_{tree}}$

3. Set Up the Proportion: $\frac{1.55}{16.8} = \frac{h_{tree}}{21.15}$

4. Solve for $h_{tree}$: Multiply both sides by $21.15$: $h_{tree} = \frac{1.55 \cdot 21.15}{16.8}$

   Calculate the values: $h_{tree} = \frac{32.7825}{16.8}$

   $h_{tree} \approx 1.95 \, \text{m}$

Final Answer:

The height of the tree is 1.95 meters to the nearest hundredth.

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Would you like additional details or have any questions?
Here are 5 related questions to expand your understanding:

1. How does the concept of similar triangles apply to this problem?
2. Can you generalize the formula for determining the height of an object using shadows?
3. What other real-life problems can be solved using similar triangles?
4. How would the answer change if Travis moved closer or farther from the tree?
5. What assumptions are made about the sun's rays in this type of problem?

Tip: Always ensure proportional relationships are set up correctly when working with similar triangles.