Find the longer diagonal of a parallelogram having sides of 10 and 15 and an angle measure of 120° between them. 13.2 18.0 21.8 23.1
Accepted Solution
A:
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