Question

如图,已知△ABC中,∠B=45°,∠C=30°,BC=4+2√3,求AB、AC的长

Answer 1

解答：
∠A=180°-∠B-∠C=105°
∴ sinA=sin105°=(√6+√2)/4
利用正弦定理：AB/sinC=AC/sinB=BC/sinA
∴ AB=BCsinC/sinA
=(4+2√3)*(1/2)/[(√6+√2)/4]
=(8+4√3)/(√6+√2)
=(6+4√3+2)/(√6+√2)
=(√6+√2)²/(√6+√2)
=√6+√2

AC=ABsinB/sinC
=(√6+√2)*sin45°/sin30°
=(√6+√2)√2
=2√3+2

Answer 2

∠A=180-B-C=105度
正弦定理：
BC/sinA=AC/sinB=AB/sinC
(4+2根号3)/sin105°=AC/sin45°=AB/sin30°
AB=根号6+根号2
AC=2+2根号3

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