How long is a string reaching from the top of a 13-ft pole to a point 11 ft from the base of the pole?

A string reaching from the top of a 14 foot poll that meets the ground 11 feet from the base of the pole is 17.03 ft long (assuming a straight, plumb pole and level ground.)

If we look at the set up here, what we have is a right triangle. The ground meets the pole at 90 degrees. Therefore, we can use Pythagorean's theorem.

The theorem tells us that, in a right triangle, the sum of the length of one leg (A) and the length of another (B) both having been squared will equal the length of the hypotenuse squared (C). Or.

A2 + B2 = C2

We've got the lengths of A and B, let's put them in.

112 + 132 = C2

121 + 169 = C2

290 = C2

Now we take the square root of both sides.

√290 = C

C ~= 17.03