how high is a tree that casts a 25 foot shadow at the same time a 6 foot pole casts a 10 foot shadow? Please help! I don't understand how to solve any problem like this!!

draw a diagram. Using similar triangles, you can see that if the tree has height h,

h/25 = 10/6

The ratio of height:shadow is the same for both pole and tree.

To solve this problem, you can use a concept called similar triangles. Similar triangles are two triangles that have the same shape but possibly different sizes.

In this case, you can consider the tree and its shadow as one triangle, and the pole and its shadow as another triangle. Since both triangles are similar, their corresponding sides are proportional.

Let's assign variables to the unknown values. Let height of the tree be 'h' and the height of the pole be 'p'. The lengths of their shadows are 25 feet and 10 feet, respectively.

Now, we can set up a proportion between the triangles:

(tree height) / (tree shadow length) = (pole height) / (pole shadow length)

So, we have:

h / 25 = p / 10

To solve for 'h', we can cross-multiply and then divide:

h = (25 * p) / 10

Now, let's substitute the known values:

h = (25 * 6) / 10

h = 150 / 10

h = 15 feet

Therefore, the height of the tree is 15 feet.