Solution:
Given:
A parallelogram ABCD.
To get the length of c, we have the sketch as shown below;
Using the side property of the parallelogram, opposite parallel sides are equal.
Hence,
[tex]\begin{gathered} a=29^{\prime} \\ b=37^{\prime} \end{gathered}[/tex]
Also, using the angle property of a parallelogram, two adjacent angles are supplementary (add up to 180 degrees).
Hence,
[tex]\begin{gathered} A+C=180^0 \\ 65+C=180 \\ C=180-65 \\ C=115^0 \end{gathered}[/tex]
A triangle ABC can be brought out from the parallelogram,
To get the length of c, we use the cosine rule;
[tex]\begin{gathered} c^2=a^2+b^2-2ab\cos C \\ \\ \text{where;} \\ a=29^{\prime} \\ b=37^{\prime} \\ C=115^0 \\ \\ \text{Hence,} \\ c^2=29^2+37^2-(2\times29\times37\times\text{cos}115) \\ c^2=2210-(2146\times\cos 115) \\ c^2=2210-(-906.9388) \\ c^2=2210+906.9388 \\ c^2=3116.9388 \\ c=\sqrt[]{3116.9388} \\ c=55.8296 \\ \\ To\text{ the nearest tenth,} \\ c=55.8^{\prime} \end{gathered}[/tex]
Therefore, the length of c to the nearest tenth is 55.8'
