Da_Gr8_Mperor Posted June 18, 2006 Share Posted June 18, 2006 One of the inside angles of a parallelogram is 60 degree. What is the ratio of the length of two diagonals? OA : 1/sqrt(3) Quote Link to comment Share on other sites More sharing options...
shud Posted June 18, 2006 Share Posted June 18, 2006 Let say X is height (minimum distance between two sides of ||gram) since 60 is one angle, sin30 = X/diaogonal1 Other angle would be 120, sin60 = X/Diagonal2 Diagonal1/Diagonal2 = sin60/sin30 = sqrt(3) Quote Link to comment Share on other sites More sharing options...
sdasar Posted June 18, 2006 Share Posted June 18, 2006 Shud, How did you assume the diagonal is bisecting the angle? You are assuming it is rhombus. I don't want to venture into trigonometry, but that is the only way we can explain this problem. Let us say one diagonal makes x degrees with base and the other diagonal makes y degrees with base. As you eluded, the ratio is sin x / sin y. Even though I believe there is a relation between x and y, sin x / sin y varies with x. I strongly believe the answer is wrong. Quote Link to comment Share on other sites More sharing options...
shud Posted June 18, 2006 Share Posted June 18, 2006 Shud, How did you assume the diagonal is bisecting the angle? You are assuming it is rhombus. I don't want to venture into trigonometry, but that is the only way we can explain this problem. Let us say one diagonal makes x degrees with base and the other diagonal makes y degrees with base. As you eluded, the ratio is sin x / sin y. Even though I believe there is a relation between x and y, sin x / sin y varies with x. I strongly believe the answer is wrong. I agree with you. yes! Quote Link to comment Share on other sites More sharing options...
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