# A triangle has two corners with angles of # pi / 4 # and # (3 pi )/ 8 #. If one side of the triangle has a length of #3 #, what is the largest possible area of the triangle?

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Two of the angles given are

Now, for the area to be as large as possible, its sides must be as large as possible. For this to happen, the one side that is specified must be the smallest one - and hence must be opposite the smallest angle - in this case

The height of this triangle

Thus the area is

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