如图,在梯形ABCD中,AD∥BC,AC⊥AB,AD=CD,cos∠DCA=45,BC=10,则AB的值是(  ) A.3 B.6 C.8 D.9

问题描述:

如图,在梯形ABCD中,AD∥BC,AC⊥AB,AD=CD,cos∠DCA=

4
5
,BC=10,则AB的值是(  )
A. 3
B. 6
C. 8
D. 9

∵在梯形ABCD中,AD∥BC,AD=CD,
∴∠DAC=∠DCA=∠ACB.
∵cos∠DCA=

4
5
,AC⊥AB,BC=10,
∴cos∠ACB=
AC
BC
=
AC
10
=
4
5

∴AC=8,AB=6.
故选B.