Two corners of a triangle have angles of #pi / 8 # and # pi / 3 #. If one side of the triangle has a length of #2 #, what is the longest possible perimeter of the triangle?
1 Answer
The maximum perimeter is:
Explanation:
When ever possible draw a diagram. It helps to clarify what you are dealing with.
Notice that I have labeled the vertices as with capital letters and the sides with small letter version of that for the opposite angle.
If we set the value of 2 to the smallest length then the sum of sides will be the maximum.
Using the Sine Rule
Ranking these with the smallest sine value on the left
So side
Set
So the maximum perimeter is: