Given a diagonal with the sides 10 and 15 units, the angle formed between them is 120.
to get the length of the longest diagonal we use the cosine rule which states that;
c^2=a^2+b^2-2abCos(C)
where a,b and c are the sides and C is the angle.
therefore let:
a=15,b=10,C=120,c=?to solve for the length C we shall substitute the values in our formula:
c^2=15^2+10^2-2*15*10 cos 120
c^2=225+100-300cos120
c^2=325-(300*(-0.5))
c^2=325-(-150)
c^2=475
getting the square root of both sides;
sqrt (c^2)=sqrt475
c=21.795
the since this is the opposite side to the largest angle, we therefore conclude that the longer diagonal of the parallelogram is 21.795 units