Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{3}$ $( pi ) / 3$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{3}$ $( pi ) / 3$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2016-04-15T23:37:29

$= 206$ $=206$

Explanation:

Let in $DeltaABC,/_A=pi/3,/_B=5pi/8$
$and /_C =(pi-pi/3-5pi/8)=pi/24$
So smallest angle $/_C=pi/24$
For having a triangle of largest perimeter , let the side of given length be the smallest side $c=14$
$a/sinA=c/sinC$
$:.a= (csinA)/sinC=14xxsin(pi/3)/sin(pi/24)~~92.9$

$b= (csinB)/sinC=14xxsin(5pi/8)/sin(pi/24)~~99.1$

So the largest possible perimeter
$a+b+c=92.9+99.1+14 =206$

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{3}$ $( pi ) / 3$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?

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Explanation:

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Two corners of a triangle have angles of (5 pi )/ 8 5π8 (5 pi )/ 8 and ( pi ) / 3 π3 ( pi ) / 3 . If one side of the triangle has a length of 14 14 14 , what is the longest possible perimeter of the triangle?

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Explanation:

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Two corners of a triangle have angles of $\frac{5 π}{8}$ $(5 pi )/ 8$ and $\frac{π}{3}$ $( pi ) / 3$ . If one side of the triangle has a length of $14$ $14$ , what is the longest possible perimeter of the triangle?