A tower subtends angles `alpha,2alpha,3alpha` respectively, at point `A , B ,a n dC` all lying on a horizontal line through the foot of the tower. Prove that `(A B)/(B C)=1+2cos2alphadot`

Explanation

To solve the problem, we will denote the height of the tower as \( h \) and the distances from the foot of the tower to points \( A \), \( B \), and \( C \) as \( d_A \), \( d_B \), and \( d_C \) respectively. The angles subtended by the tower at these points are \( \alpha \), \( 2\alpha \), and \( 3\alpha \).

### Step 1: Set up the relationships using trigonometry
From the definition of tangent in a right triangle, we can express the height of the tower in terms of the distances and angles:

1. For point \( A \):
\[
h = d_A \tan(\alpha)
...