Making roads
You are an engineer in the middle of a small and beautiful village with mountains looming in the background. They have a mud road and insist on building another thats perfectly perpendicular to the first one. Skanda's house is on the original road and the new road intersects in front of his house. Like all spirited people, they want to test your college education and give you a long rope. How do you find the right angle?
In other words, given a long rope, how can you fold it into a right-angled triangle?
I am tempted to give you a hint but GOD, someone please attempt a solution... :-)
In other words, given a long rope, how can you fold it into a right-angled triangle?
I am tempted to give you a hint but GOD, someone please attempt a solution... :-)
posted by littlecow at 9/30/2005 05:46:00 PM
6 Comments:
This might not be the original way you intended but here goes:
Tie/nail one end of the rope to one end of the road. Rotate the rope so that you get to the other end of the road with the least rope length used. This is the direction in which you want to build the second road.
To make a right-angled triangle. Once you found the above direction, nail this side too. Now both sides are nailed. Take the free end of the rope from the 2nd naiul to the 1st nail and mark this point in the nail. Unfold it and make a straight line with the rope from the 1st nail in the direction of the 2nd nail. Then, nail the rope at the marked part of the rope. Use the free end of the rope and fold it at an angle to the 3rd nail in the direction of the road at any angle. The point where it meets the road is the 4th point. Nail this point too. Then join the 2nd and the 4th points. The 1st, 2nd and 4th or the 2nd, 3rd and 4th form two right-angled triangles.
So basically you constructed a square...What if there are no nails avialable?:P ;) Then here is an alternative one...
Use the costruction steps we used in IX for constructing a perpendicular to a straight line. Basically, ask Skanda to hold one end of the rope. Carrr the other end of the rope to one some arbit distance and mark the spot on the road to the left. With the same rope length make a mark to your right. Now ask skanda to move to the spot on the left and draw a BIG arc in the general direction you want to construct the road. Now ask skanda to go to right and make another arc that intersects the BIG arc. Draw a straight line from this point to the initial position. This will be perpendicular to the road...
(I assume skanda will be there as he will be concerned that his house shouldnt be bulldozed to build a road by a whacky engineer!)
wah! libran!
wah! tripta!
Both your solutions are right and you guys lead the score table (see score table on main page!)
And there are other ways of solving this. Every new solution gets a point!
Well, actually guys, I made an isoceles triangle and not a square... 1,3, and 4 form an isoceles triangle and 2 is the bisector of the side 13. Implies 24 is at right angles to 13.
@~a~: that is another way and you get a point! there are numerous ways of doing it but i was basically looking for a pythogoras theorem solution here. this is basically a free-food question.
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