we know that in the right triangle ACD AD²=AC²+CD²-----> (√75)²+5²-----> AD²=100-----> AD=10 units sin ∠D=AC/AD----> sin ∠ D=√75/10 cos ∠D=CD/AD----> cos ∠D=5/10-----> cos ∠D=1/2
in the right triangle FDC sin ∠ D=FC/CD------> FC=CD*sin ∠ D----> FC=5*(√75)/10 FC=√75/2 units cos ∠D=FD/CD-----> FD=CD*cos ∠D-----> FD=5*(1/2)---> FD=2.5 units FD=2.5 units
AE=FD BC=AD-2*(FD)----> BC=10-2*2.5-----> BC=5 units
