Tower Height and Angle of Elevation

Let height of tower be $h$. $an \alpha = h/4$, $an \gamma = h/16$. Since angles are complementary, $an \alpha \cdot \tan \gamma = 1 \implies \frac{h^2}{64} = 1 \implies h = 8\text{ m}$. Angle of elevation from B (distance $8\text{ m}$): $an \beta = h/8 = 8/8 = 1 \implies \beta = 45^\circ$.