（2013•广州）如图所示，四边形ABCD是梯形，AD∥BC，CA是∠BCD的平分线，且AB⊥AC，AB=4，AD=6，则tanB=（）A．23B．22C．114D．554

Question

√(3)
B．2√(2)
C．(11)/(4)
D．(5√(5))/(4)√(3)

3

3
√(2)
C．(11)/(4)
D．(5√(5))/(4)√(2)

2

2
(11)/(4)
D．(5√(5))/(4)(11)/(4)111144
(5√(5))/(4)(5√(5))/(4)5√(5)5√(5)√(5)

5

544

Answer 1

∵CA是∠BCD的平分线，∴∠DCA=∠ACB，又∵AD∥BC，∴∠ACB=∠CAD，∴∠DAC=∠DCA，∴DA=DC，过点D作DE∥AB，交AC于点F，交BC于点E，∵AB⊥AC，∴DE⊥AC（等腰三角形三线合一的性质），∴点F是AC中点，∴AF=CF，∴EF...