two 22.5 degree cast iron bend are offset by 3 feet 5 inches, so the diagonal that joins them must have one hub. you need to measure a 10 foot length of 3 inch pipe and cut it for the diagonal. if you measure from the extreme end of the hub, at what dimension will you make your cut?.

Question

two 22.5 degree cast iron bend are offset by 3 feet 5 inches, so the diagonal that joins them must have one hub. you need to measure a 10 foot length of 3 inch pipe and cut it for the diagonal. if you measure from the extreme end of the hub, at what dimension will you make your cut?.

Thanks for any help!!!!

Answer 1

To determine the dimension at which you should make your cut on the 10-foot length of 3-inch pipe for the diagonal, we need to take into account the offset and the angles of the bends.

Here's how you can approach this problem step by step:

Step 1: Understand the offset
The bends are offset by 3 feet 5 inches. This means that if you were to imagine a straight line between the ends of the two bends, the line would be shifted horizontally by 3 feet 5 inches.

Step 2: Calculate the length of the diagonal
To find the length of the diagonal, you can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the diagonal) is equal to the sum of the squares of the other two sides. In this case, the two sides are the horizontal offset and the vertical distance (which is a constant 10 feet).

Using the Pythagorean theorem, you can calculate the length of the diagonal:
diagonal^2 = offset^2 + vertical distance^2

Since the vertical distance is 10 feet and the offset needs to be converted to feet as well, the equation becomes:
diagonal^2 = (3 + 5/12)^2 + 10^2

Step 3: Find the dimension for the cut
To find the dimension at which you need to make the cut on the 10-foot length of 3-inch pipe, you need to subtract the diagonal length from the total length of the pipe (10 feet).

However, before doing that, you need to account for the hub, which is the part that connects the pipe to the bend. Assuming the hub has a certain length, you need to subtract it from the total length of the pipe.

Let's say the hub length is "x" feet. Then, the equation becomes:
Cut dimension = Total length of pipe - diagonal length - hub length
Cut dimension = 10 feet - diagonal - hub

Now you have all the information you need to solve the problem. Simply calculate the diagonal length using the Pythagorean theorem, determine the hub length (if not given), and then substitute these values into the equation to find the cut dimension.

Remember, it's always a good idea to double-check your calculations and assumptions before making any cuts to ensure accuracy.