If a 5-foot post casts an 8-foot shadow at the same time that 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 about the post and its shadow, we can use the concept of similar triangles. The heights of the two objects (the post and the tree) and their corresponding shadow lengths demonstrate this relationship.

First, we establish a ratio using the height of the post and the length of its shadow:

The height of the post is 5 feet, and it casts a shadow of 8 feet. This gives us the ratio of height to shadow length for the post:

Height of the post / Shadow of the post = 5 feet / 8 feet.

Now, we apply this same ratio to the tree. Let’s denote the height of the tree as "h." The tree casts a shadow that is 48 feet long. Setting up the ratio for the tree using the known shadow length:

Height of the tree / Shadow of the tree = h / 48 feet.

Since the ratios are equal (because of similar triangles), we can set them equal to each other:

5/8 = h/48.

To solve for h, we can cross-multiply:

5 * 48 = 8 * h,

240 = 8h.

Now, divide both sides by 8 to isolate