Question

如图,△ABC,∠BAC=90°,AD⊥BC,AF是中线,AE是∠DAF的角平分线,∠CAB=90° ∠BAD：∠CAD

Answer 1

∵∠BAD：∠CAD=1:2,∠CAB=90°

∴∠BAD=30° ∠CAD=60°

∵AD⊥BC

∴∠B=60°

∵AF是Rt△ABC斜边的中线

∴AF=BF

∴∠FAB=∠B=60°

∴∠DAF=∠FAB-∠DAB=60­°-30°=30°

∵AE是∠DAF的角平分线

∴∠DAE=∠EAF=1/2∠DAF=15°

∴∠BAE=∠DAB+∠DAE=30°+15°=45°