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

To find the height of the tree, you can use the concept of similar triangles. The post and its shadow form one triangle, and the tree and its shadow form a second triangle. Since both triangles are formed by the same angles (due to the position of the sun), their corresponding sides are proportional.

The height of the post is 5 feet, and it casts a shadow that is 8 feet long. The ratio of the height to the shadow length for the post can be set up as follows:

Height of post / Length of shadow = 5 feet / 8 feet.

For the tree, you want to find its height (let's call it H) while knowing it casts a shadow of 48 feet. The same ratio applies:

Height of tree / Length of shadow = H / 48 feet.

Setting the two ratios equal, because they are proportional:

5 feet / 8 feet = H / 48 feet.

To solve for H, you can cross-multiply:

5 feet * 48 feet = 8 feet * H.

This simplifies to:

240 = 8H.

To find H, divide both sides by 8:

H = 240 / 8,

H = 30 feet.

Thus,