Two corners of a triangle have angles of #(3 pi ) / 8 # and # pi / 8 #. If one side of the triangle has a length of #3 #, what is the longest possible perimeter of the triangle?
1 Answer
First, we note that if two angles are
To maximize the perimeter the known side must be the shorter cathetus, so it is going to be opposite the smallest angle, which is
The hypotenuse of the triangle will then be:
where
while the other cathetus is:
where
Finally: