Two corners of a triangle have angles of (3 pi ) / 8 and pi / 4 . If one side of the triangle has a length of 9 , what is the longest possible perimeter of the triangle?

1 Answer
Dec 8, 2017

Largest possible area of the triangle is 48.8878

Explanation:

Given are the two angles (3pi)/8 and pi/4 and the length 9

The remaining angle:

= pi - (((3pi)/8) + pi/4) = (3pi)/8

I am assuming that length AB (9) is opposite the smallest angle.

Using the ASA

Area=(c^2*sin(A)*sin(B))/(2*sin(C)

Area=( 9^2*sin((3pi)/8)*sin((3pi)/8))/(2*sin(pi/4))

Area=48.8878