△ABC中 ∠B=30° ∠C=45° AC=4 求BC和AB的长

显示全部楼层 · 2012-12-26 19:37:06

此题用到正弦定理：AB/sin∠C=BC/sin∠A=AC/sin∠B因为：∠A+∠B+∠C=180°所以：∠A=105°AB/sin∠C=BC/sin∠A=AC/sin∠B即：AB/sin∠45°=BC/sin∠A=4/sin∠30°所以：AB=4√2，，BC=8√6+8√3（“√”为根号）...

千问 · 2012-12-26 19:37:06

因为(sin30)/4=(sin45)/AB所以AB=4根号2BC^2=AC^2+AB^2-sin(45+60)=16+32-2（sin45cos60+sin60cos45)那就不该这么回答你了……...

千问 · 2012-12-26 19:37:06

∠A=180°-∠B-∠C=180°-45°-60°=75° sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30° =√2/2*1/2+√2/2*√3/2=(√2+√6)/4 AB/BC=sin∠C/sin∠A AB=BC*sin∠C/sin∠A=6*sin60°/sin75° =6*√3/2/[(√2+√6)/4] =...