如图,在梯形ABCD中,AD∥BC,AC⊥AB,AD=CD,cosB=5/13,BC=26. 求:(1)cos∠DAC的值; (2)线段AD的长.
问题描述:
如图,在梯形ABCD中,AD∥BC,AC⊥AB,AD=CD,cosB=
,BC=26.5 13
求:(1)cos∠DAC的值;
(2)线段AD的长.
答
(1)在Rt△ABC中,∠BAC=90°,cosB=
=AB BC
.5 13
∵BC=26,
∴AB=10.
∴AC=
=
BC2−AB2
=24.
262−102
∵AD∥BC,
∴∠DAC=∠ACB.
∴cos∠DAC=cos∠ACB=
=AC BC
.12 13
(2)过点D作DE⊥AC,垂足为E,
∵AD=CD,AC=24,
∴AE=EC=
AC=12,又AD=DC,1 2
∴在Rt△ADE中,cos∠DAE=
=AE AD
.12 13
∴AD=13.