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.