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If the length of larger side of a parallelogram is $55cm$ and the one diagonal of the parallelogram makes angle of measures $30^\circ$ and $50^\circ$ with of a pair of adjacent sides find the length of the diagonal.

At least give me a base concept or start so I can solve it by my own :)


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Try drawing a picture. – Daryl Dec 31 '12 at 8:46
  1. Use the fact that "In a triangle, if side length $a < b$, then $\angle A < \angle B$". (I don't know what the name of this is, anyone has an idea?)
  2. This uniquely determines a Side Angle Angle triangle configuration in your parallelogram.
  3. Use Sine rule and Cosine rule to continue as normal.
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3. Use Sine rule and Cosine rule to continue as normal. $$$$ The sine rule suffices. – barto Dec 31 '12 at 12:32
@barto Agreed. I didn't' want to give too much away as he was asking how to solve it on his own, as I was wanted to explain how that ambiguous "larger side is 55cm" would come into play. – Calvin Lin Dec 31 '12 at 18:37

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