how long is a string reaching from the top of a 20 ft pole to a point 13 ft from the bottom of the pole?

ummmh --- 7 ft ??

To determine the length of the string, you can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite of the right angle) is equal to the sum of the squares of the other two sides.

In this case, the height of the pole acts as the longer side of the triangle (the hypotenuse), and the distance from the bottom of the pole to the point where the string is tied acts as the shorter side. We can assign these lengths as follows:

Height of the pole (longer side) = 20 ft
Distance from the bottom of the pole to the point where the string is tied (shorter side) = 13 ft

Using the Pythagorean theorem, we can find the length of the string (hypotenuse).

Applying the theorem, we can write the equation as:

Length of string (hypotenuse) = √(height^2 + distance^2)

Therefore, the length of the string equals:

Length of string = √(20^2 + 13^2)
Length of string = √(400 + 169)
Length of string = √569
Length of string ≈ 23.87 ft

Hence, the length of the string from the top of the pole to a point 13 ft from the bottom is approximately 23.87 ft.