A tree casts a shadow $32 \mathrm{ft}$ long. At the same time, the shadow cast by a vertical $5-\mathrm{ft}$ pole is $4 \mathrm{ft}$ long. Find the height of the tree The tree's height is 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 pole and its shadow form another right triangle. Since the angles are the same for both triangles, they 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 pole's height to its shadow.

Step 2 ：Let's denote the height of the tree as h. Then we can set up the following equation: \(\frac{h}{32} = \frac{5}{4}\)

Step 3 ：Solving this equation will give us the height of the tree.

Step 4 ：Final Answer: The height of the tree is \(\boxed{40}\) ft.