SOLUTION: The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72degree. Find the lengths of the sides of the parallelogram. I have 1 side which i

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Question 1036433: The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72degree.
Find the lengths of the sides of the parallelogram.
I have 1 side which is 9.1 by using the cosine rule but the second side , i do not know how to do.
Found 2 solutions by ikleyn, Theo:
Answer by ikleyn(52781) About Me  (Show Source):
You can put this solution on YOUR website!
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The diagonals of a parallelogram have lengths of 12cm and 18cm and the angle between them is 72degree.
Find the lengths of the sides of the parallelogram.
I have 1 side which is 9.1 by using the cosine rule but the second side , i do not know how to do.
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Make a sketch of the parallelogram.
Draw the diagonals.
Mark the intersection point of the diagonals.
Mark an acute angle between the diagonals. It is 72°.
Mark an obtuse angle between the diagonals. It is 180° - 72° = 108°.

Find the triangle formed by the halves of diagonals with the acute angle 72° between them.
Apply the cosine theorem to this triangle.
You will find one side of the parallelogram.

Find the other triangle formed by the halves of diagonals with the obtuse angle of 108° between them.
Apply the cosine theorem to this triangle.
You will find the other side of the parallelogram.

Notice that cos(108°) = -cos(72°).


Answer by Theo(13342) About Me  (Show Source):
You can put this solution on YOUR website!
i duplicated what i think you did and i got one of the sides of the parallelogram is equal to 9.144734256.

i used the 72 degree angle.

since the intersection of the diagonals leads to congruent vertical angles and supplementary adjacent angles, you should be able to do the same for the longer side.

the same formula can be used, only this time the angle is 108 degrees rather than 72.

you would get c^2 = 6^2 + 9^2 - 2*6*9*cos(108) which should result in c = 12.26270098 which would be the length of the other side.

that's my thinking, anyway.