A 30-foot cable is suspended between the tops of two 20-foot poles on level
ground. The lowest point of the cable is 5 feet above the ground. What is the
distance between the two poles?
To find the distance between the two poles, we can use the Pythagorean theorem.
The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
In this case, we can consider the two poles as the vertical sides of a right triangle, and the cable as the hypotenuse.
Let's call the distance between the two poles x. Then, we can draw a right triangle with a base of x, a height of 5 feet (the distance from the ground to the lowest point of the cable), and a hypotenuse of 30 feet (the length of the cable).
Using the Pythagorean theorem:
x^2 + 5^2 = 30^2
x^2 + 25 = 900
x^2 = 900 - 25
x^2 = 875
Taking the square root of both sides:
x ≈ 29.58
Therefore, the distance between the two poles is approximately 29.58 feet.