Dylan is 1.25 meters tall. At 2 p.m., he measures the length of a tree's shadow to be 34.65 meters. He stanc 30.1 meters away from the tree, so that the tip of his shadow meets the tip of the tree's shadow. Find the height of the tree to the nearest hundredth of a meter. (Diagram is not to scale.)

Step 1 ：This problem can be solved using similar triangles. The height of the tree and Dylan form the heights of two similar triangles, and the lengths of their shadows form the bases of these triangles. Therefore, the ratio of the height of the tree to Dylan's height is the same as the ratio of the length of the tree's shadow to Dylan's shadow.

Step 2 ：We can set up the following equation to solve for the height of the tree: \( \frac{height \, of \, tree}{Dylan's \, height} = \frac{length \, of \, tree's \, shadow}{length \, of \, Dylan's \, shadow} \)

Step 3 ：We know Dylan's height (1.25 meters), the length of the tree's shadow (34.65 meters), and the length of Dylan's shadow (30.1 meters). We can substitute these values into the equation and solve for the height of the tree.

Step 4 ：By substituting the values into the equation, we get \( \frac{height \, of \, tree}{1.25} = \frac{34.65}{30.1} \)

Step 5 ：Solving the equation, we find that the height of the tree is approximately 1.44 meters.

Step 6 ：Final Answer: The height of the tree is approximately \( \boxed{1.44} \) meters.