Two corners of a triangle have angles of # (3 pi )/ 8 # and # ( pi ) / 2 #. If one side of the triangle has a length of # 7 #, what is the longest possible perimeter of the triangle?

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Answer 1 · 2017-12-20T06:20:24

Longest possible perimeter of the triangle is 42.1914

Given triangle is a right angle triangle as one of the angles is #pi/2#

Three angles are #pi/2, (3pi)/8, pi/8#

To get the longest perimeter, the side of length 7 should correspond to angle #pi8# (smallest angle).

#:. a / sin A = b / sin B = c / sin C#

#7/sin (pi/8) = b/sin ((3pi)/8) =c/sin (pi/2)#

#b = (7 * sin ((3pi)/8)) / (sin (pi/8)) = 16.8995#

#c =( 7 * sin (pi/2)) / sin (pi/8) = 18.2919#

Longest possible perimeter #= (a + b + c) = 7 + 16.8995 + 18.2919 = 42.1914#