Solution: As shown in the figure, ∠ ACB = 60 and ∠ ADB = 45 are known.

∴ in Rt△ABD, BD=AB,

In Rt△ABC,

tan60 =，

∴ ,

That is BC= AB,

∫BD = BC+CD，

∴AB= AB+CD

∴ CD = ab-ab =180-180× =180-60 (m),

A: The distance between Island C and Island D is 180-60m.