A point on the hypotenuse of a triangle is at distance a and b from the sides of the triangle. Show that the maximum length of the hypotenuse is `(a^(2/3)+b^(2/3))^(3/2)`.

Explanation

To solve the problem, we will follow these steps:

### Step 1: Understand the Geometry of the Problem
We have a right triangle where a point on the hypotenuse is at distances \( a \) and \( b \) from the two sides of the triangle. We need to find the maximum length of the hypotenuse.

### Step 2: Set Up the Problem
Let \( h \) be the length of the hypotenuse. The distances from the point to the two sides of the triangle are \( a \) and \( b \). We can denote the angles at the vertices of the triangle as \( \theta \) and \( \phi \).

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