If a 5-foot post casts an 8-foot shadow and a nearby tree casts a 48-foot shadow, how tall is the tree?

To determine the height of the tree based on the given information, we can employ similar triangles. The proportions of the height of the objects to the length of their shadows remain constant under normal conditions (assuming both the post and the tree are in the same location and the light source is the same).

We know that a 5-foot post casts an 8-foot shadow. This creates a proportion between the height of the post and the length of its shadow, which can be expressed as:

Height of post / Length of post's shadow = Height of tree / Length of tree's shadow.

Substituting the known values into this formula gives us:

5 feet / 8 feet = Height of tree / 48 feet.

To solve for the height of the tree, cross-multiply:

5 feet * 48 feet = 8 feet * Height of tree.

240 feet = 8 feet * Height of tree.

Next, divide both sides by 8 feet to isolate the height of the tree:

Height of tree = 240 feet / 8 feet = 30 feet.

This calculation confirms that the height of the tree is indeed 30 feet, establishing option B as the correct answer.