MATH SOLVE

9 months ago

Q:
# 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

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