To find the height of the tree using similar triangles, we can set up a proportion based on the height and the shadow lengths of Allison and the tree.
Let:
- \( h \) = height of the tree
- Height of Allison = 5 feet
- Shadow of Allison = 2.5 feet
- Shadow of the tree = 14.5 feet
The proportion based on the similar triangles is:
\[ \frac{\text{Height of Allison}}{\text{Shadow of Allison}} = \frac{\text{Height of the tree}}{\text{Shadow of the tree}} \]
Plugging in the values, we get:
\[ \frac{5}{2.5} = \frac{h}{14.5} \]
Now, we can simplify the left side:
\[ \frac{5}{2.5} = 2 \]
So the equation becomes:
\[ 2 = \frac{h}{14.5} \]
To find \( h \), we multiply both sides by 14.5:
\[ h = 2 \times 14.5 \]
Calculating this gives:
\[ h = 29 \]
Thus, the height of the tree is 29 feet.