Question

в треугольнике abc ac=bc=12,sinb=√15/4.найдите ab

Answer 1

AC=BC=12 => углы СВА и САВ равны b
угол ВСА=180-2b

AC/sin(b)=AB/sin(180-2b) => AB=ACsin(180-2b)/sin(b)=AC*sin(2b)/sin(b)=12*2sin(b)cos(b)/sin(b)=24*cos(b)=24*sqrt(1-sin^2(b))=24*sqrt(1-sin^2(b))=24*sqrt(1-15/16)=6