Question

如图所示,要在山坡上AB两点处测量与地面垂直的铁塔CD的高,由AB两地测得塔顶C的仰角分别为60和45,AB长40米,

Answer 1

∠BCA=60-45=15

∠BAC=180-60=120

由正弦定理,得：BC=AB/sin∠BCA *sin∠BAC=40sin120/sin15

将CD延长交地面于H,因此：

CD=CH-DH=BCsin(45+30)-BHtan30

=BC sin75-BCcos75 tan30

=40sin120/sin15*(sin75-cos75tan30)

=40sin120/(sin15*cos30)*[sin75cos30-cos75sin30]

=40sin60/(sin15sin60)*sin(75-30)

=40/sin15* sin45

=40*(√6-√2)/4*√2/2

=10(√3-1)