If the angles of elevation of the top of a tower from three...

tan {30}^{o} = \dfrac{h}{x + y + z}, tan {45}^{0} = \dfrac{h}{y + z}, tan {60}^{0} = \dfrac{h}{z} ⇒ x + y + z = \sqrt{3}h ... (i) y + z = h ... (ii) z = \dfrac{h}{3}... (iii)from (ii) & (iii)y = h \left(1 - \dfrac{1}{\sqrt{3}}\right) ... (iv)from (i) & (ii)$x = \left(\sqrt{3} -1\right)$ h$... (v)\dfrac{x}{y} =\dfrac{ \left(\sqrt{3} -1\right)h}{h\left(\dfrac{\sqrt{3} - 1}{\sqrt{3}}\right)}=\dfrac{\sqrt{3}}{1}$