1.在Rt△ABC中,AB=1 AC=2 ∠A=90° AD⊥BC于D 试求(1)AD:BC (2)BD:DC2.在Rt△ABC中,∠C=90°,BC:AC=1:根号3 CD⊥AB于D,求S△CDB :S△ABC
问题描述:
1.在Rt△ABC中,AB=1 AC=2 ∠A=90° AD⊥BC于D 试求(1)AD:BC (2)BD:DC
2.在Rt△ABC中,∠C=90°,BC:AC=1:根号3 CD⊥AB于D,求S△CDB :S△ABC
答
1.1,首先求得BC=√5,显然ΔABC∽ΔABD ∴AD:AB=AC:BC∴AD=2√5/5∴AD:BC=2/51.2,又BD:AB=AB:BC∴BD=√5/5,CD=BC-BD=4√5/5∴BD:DC=1/42.∵ BC:AC=1:√3∴tanA=1/√3,A=30º,∴AB=BC/sinA=2BC,CD=ACsinA=√3/2BC...