Question

1.在Rt△ABC中,AB=1 AC=2 ∠A=90° AD⊥BC于D 试求（1）AD：BC （2）BD：DC

Answer 1

1.1,首先求得BC=√5,显然ΔABC∽ΔABD ∴AD:AB=AC:BC∴AD=2√5/5∴AD:BC=2/5

1.2,又BD:AB=AB:BC∴BD=√5/5,CD=BC-BD=4√5/5∴BD:DC=1/4

2.∵ BC:AC=1：√3

∴tanA=1/√3,A=30º,

∴AB=BC/sinA=2BC,CD=ACsinA=√3/2BC,BD=BCsinA=BC/2

∴S△CDB :S△ABC=CD*BD:CD*AB=√3/2BC*BC/2:√3/2BC*2BC=1:4