Two corners of a triangle have angles of $(5 pi )/ 12$ and $( pi ) / 12$ . If one side of the triangle has a length of $15$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-20T11:04:25

Longest possible perimeter P = 128.9363

Given :
$/_A = pi/12 , /_B = ((5pi)/12)$

$/_C = pi - pi/12 - (5pi)/12 = pi/2$

To get the longest perimeter, smallest angle should correspond to the side of length 15

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

$15/ sin (pi/12) = b / sin ((5pi)/12) = c / sin (pi/2)$

$b = (15 * sin ((5pi)/12)) / sin (pi/12) = 55.9808$

$c = (15 * sin (pi/2) ) / sin (pi/12) = 57.9555$

Perimeter P = 15 + 55.9809 + 57.9555 = 128.9363

Two corners of a triangle have angles of (5 pi )/ 12 (5 pi )/ 12 and ( pi ) / 12 ( pi ) / 12 . If one side of the triangle has a length of 15 15 , what is the longest possible perimeter of the triangle?