Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{4}$ $( pi ) / 4$ . If one side of the triangle has a length of $3$ $3$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-05T13:34:01

Largest possible perimeter of the $Delta = **15.7859**$

Sum of the angles of a triangle $=pi$

Two angles are $(5pi)/8, pi/4$
Hence $3^(rd)$ angle is $pi - ((5pi)/8 + pi/4) = pi/8$

We know $a/sin a = b/sin b = c/sin c$

To get the longest perimeter, length 3 must be opposite to angle $pi/8$

$:. 3/ sin(pi/8) = b/ sin((5pi)/8) = c / sin (pi/4)$

$b = (3 sin((5pi)/8))/sin (pi/8) = 7.2426$

$c =( 3* sin(pi/4))/ sin (pi/8) = 5.5433$

Hence perimeter $= a + b + c = 3 + 7.2426 + 5.5433 = 15.7859$

Two corners of a triangle have angles of (5 pi )/ 8 5π8 (5 pi )/ 8 and ( pi ) / 4 π4 ( pi ) / 4 . If one side of the triangle has a length of 3 3 3 , what is the longest possible perimeter of the triangle?