A triangle has two corners with angles of pi / 12 and (5 pi )/ 8 . If one side of the triangle has a length of 8 , what is the largest possible area of the triangle?

1 Answer
Dec 8, 2017

Largest possible area of the triangle is 90.6224

Explanation:

Given are the two angles (pi)/12 and (5pi)/8 and the length 8

The remaining angle:

= pi - ((pi)/12) + (5pi)/8) = (7pi)/24

I am assuming that length AB (8) is opposite the smallest angle.

Using the ASA

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

Area=( 8^2*sin((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))

Area=90.6224