Two corners of a triangle have angles of $\frac{3 π}{8}$ $(3 pi ) / 8$ and $\frac{π}{4}$ $pi / 4$ . If one side of the triangle has a length of $1$ $1$ , what is the longest possible perimeter of the triangle?

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Answer 1 · 2018-05-12T04:56:33

$color(blue)("Longest possible Perimeter of " Delta = a + b + c = 3.62 " units"$

$hat A = (3pi)/8, hat B = pi/4, hat C = pi - (3pi)/8-pi/4 = (3pi)/8$

It's an isosceles triangle with sides a & c equal.

To get the longest possible perimeter, length 1 should correspond to #hat B3, the least angle.

$;. 1 / sin (pi/4) = a / sin ((3pi)/8) = c / sin ((3pi)/8)$

$a = c = (1 * sin ((3pi)/8)) / sin (pi/4) = 1,31$

$"Perimeter of the " Delta = a + b + c = 1.31 + 1 + 1.31 = 3.62$

Two corners of a triangle have angles of (3 pi ) / 8 3π8(3 pi ) / 8 and pi / 4 π4 pi / 4 . If one side of the triangle has a length of 1 11 , what is the longest possible perimeter of the triangle?