Question 52251
The telephone pole make a right angle with the ground so we can use right triangle trigonometry.  This can be done a few ways:

We make use of the fact that sin(angle)=opposite/hypotenuse.
Let x be the guide wire and we have:
sin(45)=45ft/x
xsin(45)=x45ft/x
xsin(45)=45ft
xsin(45)/(sin(45))=45ft/(sin(45)) (Use calculator or sqrt(2)/2)
x=45ft/(.7071)
x=63.64ft

If you are required to use the pythagorean theorem only, both legs are equal for 45 degree angles and the Pythagorean Theorem states hypotenuse^2=leg^2+leg^2
x^2=45^2+45^2
x^2=2025+2025
x^2=4050
sqrt(x^2)=sqrt(4050)
x=63.64 ft