Respuesta :
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
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