We are given a diagram showing a pole with a guy wire attached to the top of it and anchored into the ground.
From the base of the pole to the bottom end of the guy tower is given as a 20-feet distance. The pole itself is 24 feet tall. The guy wire from the top of the pole to the ground forms the hypotenuse of what we can describe as a right angled triangle.
We can now use the Pythagoras' theorem to solve for the missing side (hypotenuse).
The theorem states;
[tex]c^2=a^2+b^2[/tex]
Where the variables are;
[tex]\begin{gathered} c=\text{hypotenuse} \\ a,b=\text{other sides} \end{gathered}[/tex]
We can now substitute the values given;
[tex]c^2=24^2+20^2[/tex][tex]c^2=576+400[/tex][tex]c^2=976[/tex]
Take the square root of both sides;
[tex]\sqrt[]{c^2}=\sqrt[]{976}[/tex][tex]c=31.240998\ldots[/tex]
Rounded to the nearest tenth of a foot, the length of the guy wire is;
ANSWER:
Length = 31.2 ft
The second option is the correct answer.
