A guy wire is attached 24 feet above the ground level on a telephone pole that provides support for the pole. Find the length of the wire when it meets the ground ten feet from the base of the pole.
26 ft
I think that's correct, not sure.
h^2 = 24^2 + 10^2 = 676
h = √676 = 26
you should recognize this as a multiple of the basic 5-12-13 right-angled
triangle
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 hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the guy wire forms a right triangle with the telephone pole and the ground. We are given that the guy wire is attached 24 feet above the ground level on the telephone pole. This forms the height of the triangle.
Let's label the sides of the triangle:
- The height of the triangle (guy wire) = 24 feet
- The distance from the base of the pole to the point where the guy wire meets the ground = 10 feet
- The length of the guy wire (hypotenuse) = unknown (let's call it x)
According to the Pythagorean Theorem, we have the equation:
24^2 + 10^2 = x^2
Simplifying the equation:
576 + 100 = x^2
676 = x^2
To find x, we need to take the square root of both sides of the equation:
√676 = √x^2
26 = x
Therefore, the length of the guy wire is 26 feet when it meets the ground ten feet from the base of the pole.