A 30-foot string of lights will be attached to the top of a 24-foot pole for a holiday display. How far away from the base of the pole should the end of the string of lights be anchored.
Use the Pythagorean Theorem.
A 30-foot string of lights will be attached to the top of a 24-foot pole for a holiday display. How far away from the base of the pole should the end of the string of lights be anchored.
To determine how far away from the base of the pole the end of the string of lights should be anchored, we can use the Pythagorean theorem.
Let's call the distance between the base of the pole and the anchor point of the string of lights "x".
According to the Pythagorean theorem, the sum of the squares of the two shorter sides of a right triangle is equal to the square of the longest side (the hypotenuse).
In this case, the height of the pole is one of the shorter sides (24 feet) and the length of the string of lights is the hypotenuse (30 feet). So, we have:
x^2 + 24^2 = 30^2
Simplifying the equation:
x^2 + 576 = 900
Subtracting 576 from both sides:
x^2 = 324
Taking the square root of both sides:
x = √324
x = 18
Therefore, the end of the string of lights should be anchored approximately 18 feet away from the base of the pole.
To find the distance from the base of the pole where the end of the string of lights should be anchored, you can use the Pythagorean theorem.
Let's consider a right-angled triangle formed by the string of lights, the pole, and the ground. The length of the pole represents the height of the triangle, and the string of lights represents the hypotenuse of the triangle. We need to find the length of the base, which is the distance from the base of the pole to where the string of lights is anchored.
Using the Pythagorean theorem, we have:
(base length)^2 + (height)^2 = (hypotenuse length)^2
Let's plug in the given values:
(base length)^2 + (24 feet)^2 = (30 feet)^2
Simplifying the equation:
(base length)^2 + 576 = 900
Subtracting 576 from both sides:
(base length)^2 = 324
Taking the square root of both sides:
base length = √324 = 18
So, the distance from the base of the pole where the end of the string of lights should be anchored is 18 feet.