Two corners of a triangle have angles of $(5 pi ) / 12$ and $(3 pi ) / 8$ . If one side of the triangle has a length of $8$ , what is the longest possible perimeter of the triangle?

Question

1315 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-11T05:41:41

Longest possible perimeter of the triangle is 32.8348

Given are the two angles $(5pi)/12$ and $(3pi)/8$ and the length 12

The remaining angle:

$= pi - (((5pi)/12) + (3pi)/8) = (5pi)/24$

I am assuming that length AB (8) is opposite the smallest angle

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

$8 / sin ((5pi)/24) = b / sin ((5pi)/12) = c / sin ((3pi)/8)$

$b = (8 * sin ((5pi)/12)) / sin ((5pi)/24) = 12.6937$

$c = (8*sin ((3pi)/8)) / sin ((5pi)/24) = 12.1411$

Longest possible perimeter of the triangle is = (a + b + c) / 2 =( 8 + 12.6937 + 12.1411) = 32.8348#

Two corners of a triangle have angles of (5 pi ) / 12 (5 pi ) / 12 and (3 pi ) / 8 (3 pi ) / 8 . If one side of the triangle has a length of 8 8 , what is the longest possible perimeter of the triangle?