A tree casts a shadow $24 \mathrm{ft}$ long. At the same time, the shadow cast by a vertical $4 \mathrm{ft}$ post is $12 \mathrm{ft}$ long. Find the height of the free.
The tree's height is $\mathrm{ft}$

Step 1 ：This problem can be solved using the concept of similar triangles. The height of the tree and its shadow form one right triangle, and the height of the post and its shadow form another right triangle. Since the angles are the same, these triangles are similar, and the ratios of corresponding sides are equal. Therefore, the ratio of the tree's height to its shadow is the same as the ratio of the post's height to its shadow.

Step 2 ：Let's denote the height of the tree as h. Then we can write the equation: \(\frac{h}{24} = \frac{4}{12}\)

Step 3 ：We can solve this equation to find the height of the tree.

Step 4 ：Final Answer: The height of the tree is \(\boxed{8}\) ft.