From the bottom of a pole of height h, the angle of elevation of the top of a tower is `alpha`. The pole subtends an angle `beta` at the top of the tower. find the height of the tower.

Options

A. `(hcot (alpha - beta ))/(cot (alpha - beta )- cot alpha`
B. `(h tan (alpha- beta))/(tan(alpha- beta ) - tan alpha)`
C. `(cot (alpha- beta))/(cot (alpha - beta)-cot alpha)`
D. None of these

Explanation

To find the height of the tower given the height of the pole and the angles of elevation, we can follow these steps:

### Step 1: Understand the Geometry
We have a pole of height \( H \) and a tower. The angle of elevation from the bottom of the pole to the top of the tower is \( \alpha \). The pole subtends an angle \( \beta \) at the top of the tower.

### Step 2: Set Up the Diagram
Let:
- \( O \) be the bottom of the pole.
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