At a certain time of the day, a tree 15m tall casts a shadow of 12m, while a second tree casts a shadow of 20m. how tall is that?

The two triangles created by the trees and their shadows are similar triangles. by definition the ratio created by matching sides are equal to the ratio of either of the other matching sides.

so the ratio of the shadow sides is equal to the ratio of the tree sides. the 2 shadow sides are 12 and 20 so 12/20 is the ratio. one tree side is 15 and we will say the other is x so their ratio is 15/x.

since.the 2 ratios are equal we can say:
12/20 = 15/x
12x = 300
x = 25.

so the tree is 25m tall