The CGJ girls plan to string a set of lights diagonally from two vertical poles for overhead lighting for dancing on the right side of the deck (see the diagram). The string of lights is sold in foot increments only. How many feet of diagonal lighting will need to be purchased?
What diagram?
To determine the length of diagonal lighting needed, we can use the Pythagorean theorem, which 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 vertical poles and the diagonal lighting form a right triangle, with the diagonal lighting being the hypotenuse. We need to find the length of the hypotenuse.
Let's assume the distance between the two vertical poles is x feet, and the height from the ground to the point where the diagonal lighting will be attached is y feet.
Using the Pythagorean theorem, we can write the equation as:
(x^2) + (y^2) = (diagonal lighting length)^2
Since we are given the distance between the poles, we can solve for y using the given diagram:
y = 8 feet (as shown in the diagram)
Now, we have the values of x and y. We can substitute them into the equation to solve for the diagonal lighting length:
(x^2) + (y^2) = (diagonal lighting length)^2
x^2 + 8^2 = (diagonal lighting length)^2
x^2 + 64 = (diagonal lighting length)^2
We need more information to find the exact value of x or the diagonal lighting length.
If you have the measurement of x or any additional information, please provide it, and I can help you find the exact length of diagonal lighting that needs to be purchased.