On level ground, the base of a tree is 20 ft from the bottom of a 48 - ft flagpole. The tree is shorter in the pole. At a certain time, their shadows end at the same point 60 ft from the base of the gpole. How tall is the tree?

To find the height of the tree, we can use similar triangles. Let's denote: - \( h_t \) as the height of the tree, - \( h_p = 48 \) ft as the height of the flagpole, - \( d_t = 20 \) ft as the distance from the tree to the flagpole, - \( d_p = 60 - 48 = 12 \) ft as the distance from the base of the flagpole to the end of the shadow of the flagpole. Since the shadows end at the same point, we can set up a proportion based on the similar triangles formed by the flagpole and its shadow, and the tree and its shadow. The ratio of the height of the flagpole to the length of its shadow is equal to the ratio of the height of the tree to the length of its shadow: \[ \frac{h_p}{d_p} = \frac{h_t}{d_t} \] Substituting the known values: \[ \frac{48}{12} = \frac{h_t}{20} \] Now, simplify the left side: \[ 4 = \frac{h_t}{20} \] To find \( h_t \), multiply both sides by 20: \[ h_t = 4 \times 20 = 80 \text{ ft} \] Thus, the height of the tree is \( \boxed{80} \) ft.