1. The problem is to find the altitude in a right triangle given the hypotenuse and the legs or to understand the altitude proportion theorem. 2. The altitude to the hypotenuse in a right triangle creates two smaller right triangles that are similar to the original triangle and to each other. 3. The altitude length $h$ satisfies the relation $$h^2 = p \times q$$ where $p$ and $q$ are the segments into which the hypotenuse is divided by the altitude. 4. This means the altitude is the geometric mean of the two segments of the hypotenuse. 5. For example, if the hypotenuse is divided into segments of lengths $p=4$ and $q=9$, then the altitude is $$h = \sqrt{4 \times 9} = \sqrt{36} = 6.$$