Answer :
Length of the shorter diagonal of the parallelogram will be 18.46 feet
Let the Parallelogram ABCD with BD and AC as it’s diagonal
According to the question,
AB = 17 feet
AD = 11 feet
As the opposite sides of a parallelogram are parallel and equal
Therefore, AB = CD = 17 feet
AD = BC = 11 feet
Also the longer diagonal, BD = 22 feet
In triangle BCD, using cosine formula
[tex]BD^{2}[/tex] = [tex]CD^{2}[/tex] + [tex]BC^{2}[/tex]- 2BC.CD.CosC
[tex]22^{2}[/tex] = [tex]17^{2}[/tex] + [tex]11^{2}[/tex] - 2(11)(17)Cos C
484 = 289 + 121 - 374CosC
-0.197 = Cos C
C = arc Cos(-0.197)
Therefore, C = [tex]110^{0}[/tex]
Now ∠C + ∠D = [tex]180^{0}[/tex]
101+ ∠D = 180
∠D = [tex]79^{0}[/tex]
Now, in triangle ADC
[tex]AC^{2}[/tex] = [tex]AD^{2}[/tex] + [tex]CD^{2}[/tex] - 2AD.CD.CosD
[tex]AC^{2}[/tex] = [tex]11^{2}[/tex] + [tex]17^{2}[/tex] - 2(11)(17)Cos79
[tex]AC^{2}[/tex] = 121 + 289 - 374Cos79
[tex]AC^{2}[/tex] = 410 -364(.19)
[tex]AC^{2}[/tex] = 340.84
AC = sqrt(340.84)
AC = 18.46
To know more about the diagonal of the parallelogram, visit here:
https://brainly.com/question/27064115
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