Find the measure of the longest diagonal to the nearest tenth of a centimeter:The lengths of two adjacent sides of a parallelogram are 42 cm and 36...

It is given that the lengths of two adjacent sides of a
parallelogram are 42 cm and 36 cm. One of the angles of the parallelogram is 40 degrees.
The other angle is supplementary to 40 degrees, it is equal to 180 - 40 = 140
degrees.

Divide the parallelogram into 2 triangles. One has
sides 36 and 42 and an enclosed angle of 40 degrees and the other has sides 36 and 42
and an enclosed angle of 140. The diagonal in both cases is the third
side.

Use the cosine rule which states that c^2 = a^2 + b^2
- 2*a*b*cos C

c = sqrt [a^2 + b^2 - 2*a*b*cos
C]

=> c = sqrt [ 36^2 + 42^2 - 2*36*42*cos
40]

=> 27.3
cm

and

c = sqrt [ 36^2 + 42^2
- 2*36*42*cos 140]

=> 73.3
cm

As 73.3 is larger than 27.3 that is the length of the
longer diagonal.

The length of the longer
diagonal of the parallelogram is 73.3 cm