a vertical pole 5 feet long casts a shadow of 2 feet if at the same time a nearby shadow of 10 feet how tall is the tree

From what I could gather from your incomplete sentence, you have two similar triangles created by the pole and the tree.

Use ratios.

x/10 = 5/2
x = 25

To determine the height of the tree, we can use similar triangles. Let's call the height of the tree "x" feet.

We have a vertical pole that is 5 feet tall and casts a shadow of 2 feet. We also have a nearby object that casts a shadow of 10 feet.

Using the concept of similar triangles, we can set up the following proportion:

Height of pole / Length of pole's shadow = Height of tree / Length of tree's shadow

Substituting the values we know:

5 feet / 2 feet = x feet / 10 feet

Now, let's solve for x:

(5/2) = (x/10)

To find x, we can cross-multiply:

5 * 10 = 2 * x

50 = 2x

Divide both sides by 2:

x = 50/2

x = 25

Therefore, the height of the tree is 25 feet.