In 2005, Shenyang senior high school entrance examination mathematics 22 questions detailed explanation? ! Urgent? ~ ~ ~ ~ ~ Get out of here if you don't? ! ~~

Solution: (1) passes through point B as BF⊥AD, and the extension line of intersection DA is at point F. 。

In Rt△BFA, ∠ BAF = 60,

∴BF=ABsin60 =4 3× 32=6，

AF = abcos 60 = 4 ^ 3× 12 = 2 ^ 3。

∵CD⊥AD,∠BDC=45，

∴∠BDF=45 degree,

In Rt△BFD, ∫∠BDF = 45,

∴DF=BF=6.

∴AD=DF-AF=6-2 3。

That is, the river width AD is (6-2 3) km;

(2) If the intersection point B is BG⊥CD in G, it is easy to prove that the quadrilateral BFDG is a square.

∴BG=BF=6.

At Rt△BGC, CG=BC2-BG2= 102-62=8.

∴CD=CG+GD= 14.

That is, the length of highway CD is14 km;

(3) The cable laying cost of the first scheme is low.

From (2), De = CD-Ce = 8.

∴ The laying cost of the first scheme is: 2 (DE+AB)+4ad = 400,000 yuan,

The laying cost of the second scheme is: 2(CE+BC+AB)=(32+8 3) ten thousand yuan.

∵40