Two corners of a triangle have angles of $(7 pi )/ 12$ and $pi / 4$ . If one side of the triangle has a length of $5$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-23T00:43:19

Largest possible perimeter of the triangle is 21.7304

Given $: /_ A = pi /4, /_B = (7pi)/12$

$/_C = (pi - pi /4 - (7pi)/12 ) = (pi)/6$

To get the longest perimeter, we should consider the side corresponding to the angle that is the smallest.

$a / sin A = b / sin B = c / sin C$

$5 / sin (pi/6) = b / sin ((7pi)/12) = c / sin ((pi)/4)$

$:. b = (5 * sin ((7pi)/12)) / sin (pi/6) = 9.6593$

$c = (5 * sin (pi/4)) / sin (pi/6) = 7.0711$

Longest possible perimeter $P = 5 + 9.6593 + 7.0711 = 21.7304$

Two corners of a triangle have angles of (7 pi )/ 12 (7 pi )/ 12 and pi / 4 pi / 4 . If one side of the triangle has a length of 5 5 , what is the longest possible perimeter of the triangle?