Guy wire. How long is a guy wire reaching from the top of a 24ft ploe to a point on the ground 16 feet from the pole
What is the exact length?
what is the lenght approximated to three decimal palces?
draw your triangle
the legs are 16 and 24
or, 4*4 & 4*6
so, the hypotenuse (guy wire) is 4*sqrt(16+36) = 4*sqrt(52) = 8*sqrt(13)
To find the length of the guy wire reaching from the top of a 24ft pole to a point on the ground 16 feet from the pole, we can use the Pythagorean theorem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse (the longest side) is equal to the sum of the squares of the other two sides.
In this case, the pole acts as one side of the right triangle, the distance from the pole to the ground acts as the other side, and the guy wire acts as the hypotenuse.
Using the Pythagorean theorem:
Hypotenuse^2 = side1^2 + side2^2
Hypotenuse^2 = 24^2 + 16^2
Hypotenuse^2 = 576 + 256
Hypotenuse^2 = 832
To find the exact length of the guy wire, we can take the square root of both sides:
Hypotenuse = √832
Hypotenuse = 28.844
Therefore, the exact length of the guy wire reaching from the top of a 24ft pole to a point on the ground 16 feet from the pole is approximately 28.844 feet.
To approximate the length to three decimal places, we round the decimal:
28.844 ≈ 28.844 (to three decimal places)
So, the length of the guy wire, approximated to three decimal places, is 28.844 feet.