4. 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?
diagram: mathbits(dot)com(slash)caching(slash)holiday(slash)H173740(dot)html
The Pythagorean Theorem tells you that the exact length of lighting is
√(8^2+14^2) = 16.12 feet
So, now, what's the answer you need?
To find the number of feet of diagonal lighting needed, we can use the Pythagorean theorem.
In the given diagram, the diagonal lighting forms the hypotenuse of a right triangle, with the two vertical poles as the other two sides.
Let's label the length of one vertical side as "a" and the length of the other vertical side as "b".
To find the length of the diagonal lighting (hypotenuse), we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the other two sides.
Therefore, we have the equation:
a^2 + b^2 = c^2
where c represents the length of the diagonal lighting.
Looking at the provided diagram, it seems that the length of each vertical side is approximately 12 feet.
So, using the Pythagorean theorem:
(12)^2 + (12)^2 = c^2
144 + 144 = c^2
288 = c^2
To solve for c, we take the square root of both sides of the equation:
c = √288
c ≈ 16.971
The length of the diagonal lighting, rounded to the nearest foot, is approximately 17 feet. Therefore, about 17 feet of diagonal lighting will need to be purchased.
Put less confusin wurk.
To determine the number of feet of diagonal lighting that needs to be purchased, we can use the Pythagorean theorem.
In the given diagram, there are two vertical poles forming a right triangle with the diagonal string of lights. We need to calculate the length of the hypotenuse (diagonal lighting).
Let's label the sides of the triangle as follows:
- The horizontal side (base) = a
- The vertical side (height) = b
- The diagonal side (lighting) = c (unknown, what we need to find)
According to the Pythagorean theorem, the square of the hypotenuse is equal to the sum of the squares of the other two sides:
c^2 = a^2 + b^2
Looking at the diagram, we can see that the height (b) is given as 15 feet, and the right side (a) is given as 50 feet.
Substituting these values into the equation:
c^2 = 50^2 + 15^2
Simplifying:
c^2 = 2500 + 225
c^2 = 2725
To find c, we need to take the square root of both sides:
c = √2725
c ≈ 52.15 feet
Therefore, approximately 52.15 feet of diagonal lighting will need to be purchased.