I know this problem is solved using the Pythagorean theorem.
A 1000-foot section of railroad track expands 6 inches because the day is very hot. This causes end C to break off and move to position b, forming right triangle ABC. Find BC. Note the surprising answer to this simple problem explains why railroad tracks, bridges, and similar structures must be designed to allow for expansions.
Any insight? I’m going crazy!
Do you know how long AC is? Do you know how long AB is? If you know the lengths of two sides of a right triangle, you should be able to get the lengths of the third side.
That is all of the information the problem gives.
As far as I can get is to convert to inches giving 1200 (squared) for b and 1206 (squared) for c. This leaves a. I solve for A and do not get the right answer.
a(squared)+144,000,000=144144036
a(squared)=144036
a=379.52
That is not correct. The answer the book has is 31.6.
Simple enough. Your answer is in inches. The book’s is in feet. Sometimes, you understand the problem well enough, but it’s a silly little thing that’s tripping you up.
Thank you very much.
While your here I have another question.
Find all values of x such that the distance between the given points is as indicated.
(x, 7) and (2,3) and the distance is 5
I have no clue how to solve this mostly because there is no corresponding example in the book. Am I supposed to put x in the distance formula and solve? The reason I am skeptical about this approach is that the directions imply more than one answer.
You’re right, just put it in the distance formula and solve. You will get two solutions, and here’s why. It’s for the same reason that z[sup]2[/sup] = 16 has two solutions: 4 and -4.
Cool, thanks again.
I think that is correct, Poloin99.
x can be -1 or 5 for the second one; you want a right triangle with a hypotenuse of 5. You know your y coordinates differ by 4. a[sup]2[/sup] = b[sup]2[/sup] + c[sup]2[/sup] goes to 5[sup]2[/sup] = 4[sup]2[/sup] + c[sup]2[/sup], or 25 = 16 + c[sup]2[/sup]. c[sup]2[/sup] = 9; c = +/-3
I don’t like the first problem’s answer yet, but I’ll have to come back later.
I cannot figure out from the OP what the problem actually is. If you break off a 6" hunk of track and put it at right angles, it sticks up 6". On the other hand it is pretty clear that the square root of
(1000 + 1/2)^2 - 1000^2
is approximately 31.6. I just can’t figure out how the problem could be stated to give that answer. However, if that 1000’ of track buckles in the middle and forms a triangular shape, the altitude of the triangle is exactly half that or around 15.8’. Pretty impressive.
The situation is basically what you describe at the end of your post, Hari Seldon, except that the 1000-foot length of track is just one leg of the buckling triangle, rather than being composed of two 500-foot legs.
A rail runs perpinducular from a wall to a point 1000 feet away. The rail is only attached at that point.
Due to it’s coefficient of expansion and a change in temperature, the rail expands six inches, and the rail scrapes along the wall. How far did the rail move down the wall?
It’s the best I can come up with. Warping as a triangle would make a better question.
Well, I said I’d get back to it. For the first problem, I can see the answer they want, but the presentation of the problem is poor enough that it allows multiple interpretations.