Answer:
The wire is around 10.4 meters long.
Step-by-step explanation:
This problem models a right triangle, where the legs are the height of the pole, and the horizontal distance from each guy to the base of the pole, the hypothenuse is the wire.
So, basically the problem is asking for the length of the hypothenuses, this means we can use the pythagorean theorem to find it
[tex]a^{2}=b^{2} +c^{2}[/tex]
Where [tex]a[/tex] represents the length of the wire, [tex]b[/tex] represents the height of the pole and [tex]c[/tex] represents the horizontal distance between the guy wire and the base of the pole.
According to the problem [tex]b=10[/tex] and [tex]c=3[/tex], replacing these values, we have
[tex]a^{2}=10^{2} +3^{2}=109\\a=\sqrt{109}\approx 10.4[/tex]
Therefore, the wire is around 10.4 meters long.
