Two corners of a triangle have angles of $pi / 8$ and $pi / 8$ . 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 · 2018-01-27T04:12:20

Longest possible perimeter of the triangle $P = color(blue)(26.9343)$

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Third angle $C = pi - (pi/8) + (pi/8) = (3pi)/4$

It is an isosceles triangle with sides a, b equal.

Length 7 should correspond to the least angle $(pi/8)$

Therefore, $a / sin A = b/ sin B = c / sin C$

$c / sin ((3pi)/4) = 7 / sin (pi/8) = 7 / sin (pi/8)$

$c = (7 * sin ((3pi)/4)) / sin (pi/8) = 12.9343$

Longest possible perimeter of the triangle

$P = (a + b + c) = 12.9343 + 7 + 7 = color(blue)(26.9343)$

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