Arhombus has sides 10 cm long and an angle of 60°. find the diagonals of the rhombus.

See the attached figure to better understand the problem

we know that
in a rhombus the diagonals bisect each other at a right-angle, and that all sides are equal

in the triangle AOB
AO=AB*cos 60°---------> AO=10*(1/2)--------> AO=5 cm
so
diagonal AC=AO*2---------> AC=5*2------> 10 cm

and
BO=10*sin 60°----------> BO=10*(√3)/2------> BO=5√3 cm
so
diagonal BD=BO*2---------> BD=(5√3)*2------>BD=10√3 cm

the answer is
the diagonals are
AC=10 cm
BD=10√3 cm