A vertical tower sands on a horizontal plane and is surmounted by a vertical flag staff of height `hdot` At a point on the plane, the angles of elevation of the bottom and the top of the flagstaff are `alpha` and `beta` .Prove that the height of the tower `(htanalpha)/(tanbeta-tanalpha)`

Explanation

To solve the problem, we need to find the height of the tower (let's denote it as \( h_t \)) in terms of the height of the flagstaff \( h \) and the angles of elevation \( \alpha \) and \( \beta \).

### Step-by-Step Solution:

1. **Identify the Elements**:
- Let \( O \) be the point on the ground where the observer is standing.
- Let \( A \) be the top of the tower.
- Let \( B \) be the bottom of the flagstaff (which is also the top of the tower).
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