Answer:
They would need 1.82 meters of cable, approximately.
Step-by-step explanation:
According to the problem, the line segment BC is the closest power line. So, the lightning contractors should connect the new light A to the closest point of the power line, which is C, you can see this in the image attached.
To know the total length of cable they need, we must find the distance from point A to point C with the following formula
[tex]d=\sqrt{(y_{2} -y_{1} )^{2} +(x_{2} -x_{1} )^{2} }[/tex]
Where [tex]A(6,19)[/tex] and [tex]C(12,10)[/tex], replacing coordinates, we have
[tex]d_{AC}=\sqrt{(10-19)^{2} +(12-6)^{2} }=\sqrt{(-9)^{2}+(6)^{2} } =\sqrt{81+36}=\sqrt{117}\\d_{AC} \approx 1.82 \ m[/tex]
Therefore, they would need 1.82 meters of cable, approximately.
