A triangle has two corners with angles of $pi / 12$ and $(7 pi )/ 8$ . If one side of the triangle has a length of $11$ , what is the largest possible area of the triangle?

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Answer 1 · 2018-01-24T11:52:25

Largest possible area of the triangle $A_t = color(green)(41.9086)$

Given : $/_A = pi/12, /_B = (7pi)/8$

Third angle $C = pi - pi/12 - (7pi)/8 = pi/24$

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To get largest area, side c should be equal to length 11 as $/_C$ is the smallest.

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

$a / sin (pi/12) = b / sin ((7pi)/8) = 11 / sin (pi/24)$

$a = (11 * sin (pi/12)) / sin (pi/24) = 21.8118$

$b = (11 * sin ((7pi)/8)) / sin (pi/24) = 32.2504$

Area of the triangle $Delta ABC = A_t = (a * b * sin C) / 2$

$A_t = (21.8118 * 32.2504 * sin (pi/24)) / 2 = color(green)(41.9086)$

A triangle has two corners with angles of pi / 12 pi / 12 and (7 pi )/ 8 (7 pi )/ 8 . If one side of the triangle has a length of 11 11 , what is the largest possible area of the triangle?