The base of a ladder is 14 feet away from the wall. The top of the ladder is 17 feet from the floor. Find the length of the ladder to the nearest thousandth.
length^2=14^2 + 17^2
To find the length of the ladder, we can use the Pythagorean theorem, which 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 other two sides.
In this case, the base of the ladder forms one side of the right triangle, while the height of the ladder forms the other side. The distance from the base of the ladder to the wall is given as 14 feet, and the distance from the top of the ladder to the floor is given as 17 feet.
Applying the Pythagorean theorem, we can calculate the length of the ladder:
length^2 = 14^2 + 17^2
length^2 = 196 + 289
length^2 = 485
To find the length itself, we need to take the square root of both sides of the equation:
length = √485
Using a calculator, we find that the square root of 485 is approximately 22.022. Therefore, the length of the ladder is approximately 22.022 feet to the nearest thousandth.