Aflagpole broke in a storm. 7 meters are still sticking straight out of the ground, where it snapped, but the remaining piece has hinged over and touches the ground at a point 24 meters away horizontally.
how tall was the flagpole before it broke?

32 meters tall.
It would form a right triangle, in which the shorter leg is 7m and the longer leg is 24m.  You're looking for the last side, the hypotenuse.  So use the Pythagorean theorem. a^2 + b^2 = c^2 , in which a and b are the legs and c is the hypotenuse.
Therefore, you get 7^2 + 24^2 = c^2.
Which is, 49 + 576 = c^2
Add, 625 = c^2.
Take the square root of 625, which is 25.   So, the length of the hypotenuse (last side) is 25m.  Add the 7m that is sticking out of the ground, to get 32m.

The broken part forms the hypotenuse of a right angled triangle.

So we have a right angled triangle, the vertical part is 7m, and the horizontal is 24m.

From Pythagoras' Theorem:

x² = 24² + 7²

x² = 576 + 49

x² = 625

x = √625

x = 25

So the broken part is 25m long.

The length of the flagpole before it was broken =  25 + 7

= 32m.

Really beautiful question.

A. is the answer in this question