To find the height of the tree, we can use the concept of similar triangles. The ratio of the height of the man to the length of his shadow is the same as the ratio of the height of the tree to the length of its shadow.
Let \( h \) be the height of the tree. We have:
- Height of the man = 2 m
- Length of the man's shadow = 4 m
- Length of the tree's shadow = 6 m
We can set up the following proportion:
\[ \frac{\text{Height of the man}}{\text{Length of the man's shadow}} = \frac{\text{Height of the tree}}{\text{Length of the tree's shadow}} \]
Substituting in the values:
\[ \frac{2}{4} = \frac{h}{6} \]
Now, we can cross-multiply to solve for \( h \):
\[ 2 \cdot 6 = 4 \cdot h \]
\[ 12 = 4h \]
Now, divide both sides by 4:
\[ h = \frac{12}{4} = 3 \]
Therefore, the height of the tree is \( \boxed{3} \) meters.
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