Question

已知,如图在△ABC中,∠ABC＝45° ,∠ACB＝60° ,D在AC的延长线上,AB＝√6 CD.

Answer 1

解

作AE⊥BC于点E

设CE=1

∵∠ACE =60°

∴∠CAE =30°

∴AC =2

∴AE =√3

∵∠ABC =45°

∴△ABE 是等腰直角三角形

∴AB=√6

∵AB=√6CD

∴CD=1

∴CD=CE

∵∠ACB=60°

∴∠CED=∠ECD=30°

∴AE=DE=BE

∴∠DBC=15°