we know that
to get the length of the longest diagonal we use the cosine rule which states that----------> c²=a²+b²-2abCos(C)
where a,b and c are the sides and C is the angle.
therefore
a=15,b=10,C=120,c=?
to solve for the length C we shall substitute the values
c²=15²+10²-2*15*10*cos 120
c²=225+100-300*cos120
c²=325-(300*(-0.5))
c²=325-(-150)c²=475
c=√475
c=21.79-------------> c=21.8 units
since this is the opposite side to the largest angle, we therefore conclude that the longer diagonal of the parallelogram is 21.8 units
the answer is 21.8 units