Two corners of a triangle have angles of $(3 pi ) / 4$ and $pi / 6$ . If one side of the triangle has a length of $6$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-09T01:38:12

Longest possible perimeter $=33.9854$

Angles are $(3pi)/4, (pi/6), (pi/12)$
Length of smallest side $=6$
$:.6/sin(pi/12)=b/sin((3pi)/4)=c/sin(pi/6)$

$b=(6*sin((3pi)/4))/sin(pi/12)$
$b=4.2426/0.2588=16.3934$

$c=(6*sin(pi/6))/sin(pi/12)$
$c=$ 3/0.2588= $11.5920$

Longest possible perimeter $=6+16.3934+11.5920=33.9854$

Two corners of a triangle have angles of (3 pi ) / 4 (3 pi ) / 4 and pi / 6 pi / 6 . If one side of the triangle has a length of 6 6 , what is the longest possible perimeter of the triangle?