A moving conveyor is built to rise 4 ft for each 5 ft of horizontal change.
Suppose the conveyor runs between two floors in a factory. Find the length of the conveyor if the vertical distance between floors is 8 feet. (Round your answer to three decimal places.)
ratio problem
length : height = 5 : 4 = L : 8
5/4 = L/8
4L = 40
L = 10
I misread the question.
We still have to use my previous answer.
let the belt be x ft long, the other two sides of the right-angled triangle are
8 feet and 10 feet.
x^2 = 8^2 + 10^2
= 164
x = √164
use your calculator, and round the answer to the accuracy required.
It says I have to use Pythag and the answer will be a decimal number
Thank you!!!
To find the length of the conveyor, we can use the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the vertical distance between floors is the height of the right triangle and the horizontal change is the base of the right triangle. Let's denote the height as h and the horizontal change as b.
Given that the vertical distance is 8 feet and the conveyor rises 4 feet for each 5 feet of horizontal change, we can set up the following ratio:
4/5 = h/b
To find h, we can rearrange the equation as follows:
h = (4/5) * b
Now, we can apply the Pythagorean theorem:
h^2 + b^2 = length^2
Substituting the expression for h, we have:
((4/5) * b)^2 + b^2 = length^2
Simplifying the equation:
(16/25) * b^2 + b^2 = length^2
Combining like terms:
(41/25) * b^2 = length^2
Taking the square root of both sides to solve for length:
length = √((41/25) * b^2)
Now we can substitute the known value for b, which is 5 feet:
length = √((41/25) * (5^2))
Simplifying:
length = √((41/25) * 25) = √41
Therefore, the length of the conveyor is approximately 6.403 feet (rounded to three decimal places).