Guy wire. How long is a guy wire reaching from the top of a 24ft pole to a point on the ground 16 ft from the pole?
Thank you.
To find the length of the guy wire, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (in this case, the guy wire) is equal to the sum of the squares of the lengths of the other two sides.
In this case, the height of the pole forms one side of the right triangle, measuring 24 ft. The distance from the pole to the point on the ground forms the other side, measuring 16 ft. So we can set up the equation as follows:
Hypotenuse^2 = Height^2 + Distance^2
Let's plug in the known values:
Hypotenuse^2 = 24^2 + 16^2
Hypotenuse^2 = 576 + 256
Hypotenuse^2 = 832
To find the length of the guy wire, we need to take the square root of both sides:
Hypotenuse = √832
Using a calculator, we find that the square root of 832 is approximately 28.84.
Therefore, the length of the guy wire reaching from the top of the 24 ft pole to a point on the ground 16 ft from the pole is approximately 28.84 ft.