A triangle has two corners with angles of $pi / 4$ and $(3 pi )/ 8$ . If one side of the triangle has a length of $5$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-01-07T03:33:52

Longest possible perimeter $color(green)(P_t = 18.0656)$

Given
$D = pi /4, E = (3pi)/8, F = pi - D - E = pi - pi/4 - (3pi)/8 = (3pi)/8$

$E = F = (3pi)/8$

It’s an isosceles triangle.

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To get the longest perimeter, length 5 should correspond to the smallest angle $D (pi/4)$

$e / sin E = d / sin D$

$e = (5 * sin ((3pi)/8)) / sin (pi/4) = color (blue)(6.5328)$

Longest possible perimeter $color(green)(P_t )= 5 +( 2 * 6.5328)) color (green)(= 18.0656)$

A triangle has two corners with angles of pi / 4 pi / 4 and (3 pi )/ 8 (3 pi )/ 8 . If one side of the triangle has a length of 5 5 , what is the largest possible area of the triangle?