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=
,BC=10,则AB的值是( )4 5
A. 3
B. 6
C. 8
D. 9
答
∵在梯形ABCD中,AD∥BC,AD=CD,
∴∠DAC=∠DCA=∠ACB.
∵cos∠DCA=
,AC⊥AB,BC=10,4 5
∴cos∠ACB=
=AC BC
=AC 10
,4 5
∴AC=8,AB=6.
故选B.