I have this application that I cant figure out how to work. Please help without giving me the answer.

A tree casts a shadow that measures 5 m. At the same time, a meter stick casts a shadow that is 0.4 m long. How tall is the tree?

Since the meter stick's shadow is 0.4 of its actual length, then the tree's shadow must be 0.4 of its actual length.

Let x = height of tree.

0.4x = 5
x = ?

To find the height of the tree, we can use the concept of similar triangles. Similar triangles have proportional sides.

Step 1: Identify the corresponding sides of the triangles:
In this case, the height of the tree and the length of its shadow form one pair of corresponding sides, while the height of the meter stick and the length of its shadow form the other pair.

Step 2: Set up a proportion:
We can set up a proportion based on the corresponding sides. Let's use "x" to represent the height of the tree:
(tree height) / (tree shadow length) = (meter stick height) / (meter stick shadow length)

So, we have:
x / 5 = 1 / 0.4

Step 3: Solve the proportion:
To solve the proportion, we can cross-multiply and then solve for "x":
0.4x = 5 * 1

Step 4: Evaluate the expression:
0.4x = 5

Step 5: Solve for "x":
Divide both sides of the equation by 0.4:
x = 5 / 0.4

Step 6: Perform the calculation:
x = 12.5

Therefore, the height of the tree is 12.5 meters.