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Mumz [18]
3 years ago
7

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 fe

nce 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.
Mathematics
1 answer:
Iteru [2.4K]3 years ago
5 0

Answer:

The amount required is  l_t  =  1586 \ m

Step-by-step explanation:

From the question we are told that

   The length of one side is  l_1 =  435 \ m

    The length  of the second side is  l_2  =  656 \  m

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

Generally using cosine rule the third side is evaluated as

     l_3^2 =  l_1 ^2  + l_2^2  -  2 * l_1  *  l_2  cos  (\theta )

=>    l_3^2  =  435 ^2  +  656^2  -  2 * 453* 656 cos (49)

=>   l_3  =  495 \  m

The total  amount of face required is  mathematically evaluated as

       l_t   = l_1  + l_2 + l_3

   l_t  =  435 +  656 +  495

   l_t  =  1586 \ m

     

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