Question

已知△ABC中,∠B=45°,∠BAC=75°,AC=4求AB和BC

Answer 1

过点A作AD⊥BC于点D

∵ ∠B=45°,∠BAC=75°且,∠B+∠BAC+∠C=180°

∴∠C=60°

∴∠DAC=30°,∠BAD=45°

CD/AC=sin∠DAC AD/AC=cos∠DAC

CD=1/2( sin∠DAC)=2 AD=AC*cos∠DAC =2√3

∵ ∠B=∠BAD=45°

∴AD=BD

BD=2√3

AB=BDsin∠BAD=2√6

BC=2+2√3

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