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

Question

1471 views around the world

You can reuse this answer
Creative Commons License

Answer 1 · 2017-12-26T10:38:39

Longest possible perimeter of the triangle is 21.5447

Given $: /_ A = pi /4, /_B = (pi)/3$

$/_C = (pi - pi /4 - (pi)/3 ) = (5pi)/12$

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

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

$6 / sin (pi/4) = b / sin ((5pi)/12) = c / sin ((pi)/3)$

$:. b = (6 * sin ((5pi)/12)) / sin (pi/4) = 8.1962$

$c = (6 * sin (pi/3)) / sin (pi/4) = 7.3485$

Longest possible perimeter $P = 6 + 8.1962 + 7.3485 = 21.5447$

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