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 $12$ $12$ , 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 $12$ $12$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-10-18T02:17:25

Longest possible perimeter $= 142.9052$ $= 142.9052$

Explanation:

Three angles are $\frac{π}{3}, \frac{5 π}{8}, (π - (\frac{π}{3} + \frac{5 π}{8})$ $pi/3, (5pi )/ 8, (pi - (pi/3+(5pi)/8)$
= $\frac{π}{3}, \frac{5 π}{8}, \frac{π}{24})$ $pi/3, (5pi)/8, pi/24)$

To get longest possible perimeter, length 12 should correspond to least angle $\frac{π}{24}$ $pi/24$
$:. 12/sin (pi/24) = b / sin ((5pi)/8) = c / sin (pi/3)$

$c = (12* sin(pi/3)) / sin (pi/24) = 45.9678$
$b = (12 * (sin (5pi)/8))/sin (pi/24) = 84.9374$

Perimeter $= 12 + 45.9678 + 84.9374 = 142.9052$

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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 $12$ $12$ , what is the longest possible perimeter of the triangle?

1 Answer

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 12 12 12 , 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 $12$ $12$ , what is the longest possible perimeter of the triangle?