1. Identify the parallelogram as [tex] ABCD [/tex].
2. The diagonal divides it into two congruent triangles, so let's take only the triangle [tex] ABD [/tex], where [tex] BD [/tex] is the diagonal.
3. Now, you must apply the Law of Cosines:
[tex] c=\sqrt{a^{2}+b^{2}-2abCos(C)} [/tex]
Where [tex] a=40ft; b=70 ft [/tex] and [tex] C [/tex] is the angle between [tex] A [/tex] and [tex] B [/tex].
4. [tex] C [/tex] and [tex] 36 degrees [/tex] are suplementary. Therefore:
[tex] C=180degrees-36degrees=144degrees [/tex]
5. Substitute values into the formula:
[tex] c=\sqrt{40^{2}+70^{2}-2(40)(70)Cos(144)} =105ft [/tex]
The answer is: [tex] 105ft [/tex]
