ABCDEF is a regular hexagon. Two poles are erected at C and D, which subtend angles of elevation 30° and 45° at A respectively. What is the ratio of height of pole at C to the one at D?

1 : 2

At pole D,

tan 45° = 1  :  1 (using ratios to solve tan∮)

                      ↓

               ↓       2 (diagonal)

                2

At pole C,

tan 30° = 1  :  \(\sqrt{3}\)

                          ↓

                ↓     \(\sqrt{3}\) (diagonal)

                1

Ratio = 1 : 2