Question 1036433
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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°).