Perimeter of the plot of land = 1,920 m.
Perimeter = sum of all the sides of the triangular plot of land.
We only know two of the sides, therefore, we would find the third side length by applying the Law of Cosines, which is:
[tex]c^2 = a^2 + b^2 - 2ab \times Cos $ C[/tex]
Where,
[tex]c = $ third $ side $ = ?\\a = 345\\b = 780\\C = 79.8[/tex]
Substitute the values into the formula:
[tex]c^2 = 345^2 + 780^2 - 2(345)(780) \times Cos $ 79.8\\c^2 = 727,425- 538,200 \times 0.1771\\c^2 = 632,109.78\\c = \sqrt{632,109.78} \\\c = 795.1[/tex]
The third side is 795.1 m long.
Therefore:
Perimeter = [tex]345 + 780 + 795 = 1,920$ m[/tex]
The perimeter of the plot of land is 1,920 m.
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