The discussion centers on calculating the length of segment XY in a rectangular diagram, with participants debating the correctness of the proposed answer of 1. The consensus is that if the rectangle's corner angles are all equal (specifically 45 degrees), the length can be derived without complex calculations. The cosine rule, similarity, and properties of isosceles right triangles are highlighted as key concepts in solving the problem, ultimately leading to the conclusion that the length of XY is indeed 1, based on the assumption of equal angles and known side lengths of 6 and 11.
PREREQUISITESStudents, educators, and anyone interested in geometry, particularly those looking to enhance their problem-solving skills in calculating lengths and angles in rectangular diagrams.
I disagree. A simple approach is generally better than one that is more complicated. What's the value in doing calculations that don't need to be done?chwala said:I appreciate your approach ...its good but I think my approach would be better for students who may want to find value of the length segment ##YX## by way of calculations...cheers
The problem was rigged to be solvable without any significant calculations. I'm afraid that your method is not using the principles that the problem was made to exercise. And I am not sure that you understood what many people were trying to tell you about the simpler solution.chwala said:I appreciate your approach ...its good but I think my approach would be better for students who may want to find value of the length segment ##YX## by way of calculations...cheers
Mark44 said:I disagree. A simple approach is generally better than one that is more complicated. What's the value in doing calculations that don't need to be done?
FactChecker said:The problem was rigged to be solvable without any significant calculations. I'm afraid that your method is not using the principles that the problem was made to exercise. And I am not sure that you understood what many people were trying to tell you about the simpler solution.
phinds said:I strongly agree w/ both of these. @chwala, you seem to have missed the point of the exercise.
##8.485## is indeed the length of the hypotenuse, but it is not ##\sqrt{5.5^2+6^2}##. How did you arrive at ##8.485## ?chwala said:Square root of ## 5.5^2 + 6^2##
hmmm27 said:##8.485## is indeed the length of the hypotenuse, but it is not ##\sqrt{5.5^2+6^2}##. How did you arrive at ##8.485## ?
The main thing that makes this problem "complicated." Is not that its a hard problem. As I believe phinds pointed out, is that the use of the "circle" marks on the diagram implies that those angles are congruent. I believe some users, including myself, are more familiar with the tick markings to illustrate angles are congruent.chwala said:aaaaaaaarrgh...i made the same mistake just like the silly mistakes i make in chess,... sorry that was very silly of me ..to respond without thinking.
i used SOHCAHTOA,##cos 45^0##=##\frac {6}{h}##
##h##=##\frac {6}{cos 45^0}##=##8.485281374##
Oh, okay, now that makes sense.chwala said:aaaaaaaarrgh...i made the same mistake just like the silly mistakes i make in chess,... sorry that was very silly of me ..to respond without thinking.
i used SOHCAHTOA,##cos 45^0##=##\frac {6}{h}##
##h##=##\frac {6}{cos 45^0}##=##8.485281374##