In ΔEDC, tan 30° = \text{ED}\over \text{DC}

or, 1\over √3 = \text{AE - AD}\over \text{CD} — (1)

In ΔEAB,

tan 60° = \text{AE}\over \text{AB}

or, √3 = \text{AE}\over \text{CD} — (2)

Divide (1) by (2),

\text{AE - AD}\over \text{AE} = 1\over √3 × 1\over √3

or, {\text{AE}\over \text{AE}} - {\text{AD}\over \text{AE}} = 1\over 3

or, 1 – {\text{AD}\over \text{AE}} = 1\over 3

or, {\text{AD}\over \text{AE}} = 1 – 1\over 3

or, {\text{AD}\over \text{AE}} = 2\over 3

or, {\text{BC}\over \text{AE}} = 2\over 3

or, {\text{AE}\over \text{BC}} = 2\over 3

The ratio of the heights of building and lamp post = 3 : 2