用正弦定理吧!
sin∠A /a = sin∠B/b = sin∠C/c
C=90°,B=75°,c=4 代入,即
sin75°/b=sin90°/4 √2 √3
又sin75°=sin(45°+30°)=sin45°cos30°+cos45°sin30°= (=√6+√2)/4故 b=√6+√2