The Ladder

Right triangles hide in everyday problems. A ladder leaning on a wall makes one: the wall is upright and the ground is flat, so they meet at a right angle. The ladder is the slanted side, the hypotenuse.

A 10 m ladder with its foot 6 m from the wall reaches up the wall to a height h with ${6}^{2}+{h}^{2} = {10}^{2}$. So ${h}^{2} = 64$ and the ladder reaches 8 m up. The story gives you the triangle; the theorem does the rest.

Before reaching for a formula, mark where the right angle is. Everything follows from that: the hypotenuse faces it.