Seeing Bcsin ∠ BDC = CDs in ∠ CBD from sine theorem

So BC = CDs in ∠ BDC sin ∠ CBD = 30× sin60sin45 =156.

In Rt△ABC, ∠ ACB = 60,

∴ab=bctan∠acb= 156tan60 = 452

So the answer is: 452.