Two corners of a triangle have angles of # (2 pi )/ 3 # and # ( pi ) / 6 #. If one side of the triangle has a length of # 5 #, what is the longest possible perimeter of the triangle?
1 Answer
Nov 13, 2016
The longest possible perimeter is,
Explanation:
Let
Let
Then
To obtain the longest perimeter, we associate the given side with the smallest angle but we have two angles that are equal, therefore, we shall use the same length for both associated sides:
side
We may use the Law of Cosines to find the length of side b:
The longest possible perimeter is,