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A farmer has a field in the shape of a triangle. The farmer has asked the manufacturing class at your school to build a metal fence for his farm. From one vertex, it is 435m to the second vertex and 656m to the third vertex. The angle between the lines of sight to the second and third vertices is 49 degrees. Calculate how much fencing he would need to enclose his entire field.

Answer :

okpalawalter8

Answer:

The amount required is  [tex]l_t = 1586 \ m[/tex]

Step-by-step explanation:

From the question we are told that

   The length of one side is  [tex]l_1 = 435 \ m[/tex]

    The length  of the second side is  [tex]l_2 = 656 \ m[/tex]

     The angle between the line of sight of second and third side is  [tex]\theta = 49^o \\[/tex]

Generally using cosine rule the third side is evaluated as

     [tex]l_3^2 = l_1 ^2 + l_2^2 - 2 * l_1 * l_2 cos (\theta )[/tex]

=>    [tex]l_3^2 = 435 ^2 + 656^2 - 2 * 453* 656 cos (49)[/tex]

=>   [tex]l_3 = 495 \ m[/tex]

The total  amount of face required is  mathematically evaluated as

       [tex]l_t = l_1 + l_2 + l_3[/tex]

   [tex]l_t = 435 + 656 + 495[/tex]

   [tex]l_t = 1586 \ m[/tex]

     

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