At sunset, a tree projects a shade that is 2.5 meters of length. The distance from the tree top to the most distant end of the shade is 4 meters.
What is height of the tree?

3.12 meters.

We imagine a right triangle with base b, that is the shade of the tree. Its height a, is the height of the tree and its hypotenuse, h, is the distance from the top of the tree to the end of the shade.
Since the triangle is right, we apply the Pythagorean theorem to calculate its height:
h^2 = a^2 + b^2
4^2 = a^2 + (2.5)^2
16 - 6.25 = a^2
9.75 = a^2
a = sqrt(9.75)
a = 3.12