Two corners of a triangle have angles of $(5 pi )/ 8$ and $( pi ) / 6$ . If one side of the triangle has a length of $2$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-11T07:45:19

Largest possible area of the triangle is **2.2497

Given are the two angles $(5pi)/8$ and $pi/6$ and the length 7

The remaining angle:

$= pi -( ((5pi)/8) + pi/6) = (5pi)/24$

I am assuming that length AB (2) is opposite the smallest angle.

Using the ASA

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

Area $=( 2^2*sin((5pi)/24)*sin((5pi)/8))/(2*sin(pi/6))$

Area $=2.2497$

Two corners of a triangle have angles of (5 pi )/ 8 (5 pi )/ 8 and ( pi ) / 6 ( pi ) / 6 . If one side of the triangle has a length of 2 2 , what is the longest possible perimeter of the triangle?