Elevation angle of the top of the mirror from the foot of the tower of height $h$ is $\alpha$ and the tower subtend an angle $\beta$ at the top of the mirror. Then, height of mirror is

Let the height of the mirror be x, making its top situated x units above the ground while the tower of height h stands vertically. From the foot of the tower, the angle of elevation to the top of the mirror establishes the horizontal distance between the structures as x divided by tan alpha, which is x cot alpha. Because the mirror's top subtends an angle beta at the top of the tower, the vertical height difference between them is (h - x), allowing the relationship tan beta = (h - x) / (x cot alpha). Rearranging this yields (h - x) = x cot alpha tan beta, and since the angle of depression from the mirror to the tower base is alpha, the angle inside the relevant triangle is (alpha - beta), transforming the equation to x = h cot (alpha - beta) / (cot (alpha - beta) - cot alpha).

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