Question

如图,A,B是公路l（l为东西走向）两旁的两个村庄,

Answer 1

设定直线AB交叉直线L于O,

既然B村在A村的南偏东45°方向上,

AC = CO ；BD = DO

CO = 1 ；DO = 2

AO = √(AC² + CO²)

= √(1 + 1)

= √2

BO = √(BD² + DO²)

= √(2 + 2)

= 2

AB的距离为 AO + BO

= (√2) + 2

= 1.4142 + 2

= 3.4142 km

P点是AB的中间,也就是,

AP = BP = (2 + √2)/2 = 1.7071

拉长AC的直线,并从P点向西画条直线交叉拉长过后的AC直线,并交叉于Q.

AQ的长度是,

AP = √(AQ² + PQ²) ,AQ = PQ

AP² = 2AQ²

AQ = AP/√2

AQ = 1.4142 = PQ

CQ = AQ - AC

= 1.4142 - 1

= 0.4142

CP = √(CQ² + PQ²)

= √(0.1716 + 2)

= √2.1716

= 1.4736km