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)#