Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{12}$ $( pi ) / 12$ . If one side of the triangle has a length of $5$ $5$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-05T12:47:18

Largest possible area of the $Delta = color (purple)(27.1629)$

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

The remaining angle:

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

I am assuming that length AB (5) is opposite the smallest angle.

Using the ASA

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

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

Area $=27.1629$

Two corners of a triangle have angles of (5 pi )/ 8 5π8 (5 pi )/ 8 and ( pi ) / 12 π12 ( pi ) / 12 . If one side of the triangle has a length of 5 5 5 , what is the longest possible perimeter of the triangle?