From a point on the ground at a distance `a` from the foot of a pole, a ball is thrown at an angle of `45^@`, which just touches the top of the pole and strikes the ground at a distance of `b`, on the outer side of it. Find the height of the pole.

Explanation

To find the height of the pole, we can follow these steps:

### Step 1: Understand the Geometry of the Problem
We have a pole of height \( h \) and a ball is thrown from a point on the ground at a distance \( a \) from the foot of the pole. The ball is thrown at an angle of \( 45^\circ \) and it just touches the top of the pole before striking the ground at a distance \( b \) from the pole.

### Step 2: Set Up the Coordinate System
Let’s set up a coordinate system where:
- The foot of the pole is at the origin (0, 0).
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