A triangle has two corners with angles of $pi / 4$ and $(5 pi )/ 8$ . If one side of the triangle has a length of $3$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-11T06:59:13

Largest possible area of the triangle is 7.682

Given are the two angles $(5pi)/8$ and $pi/4$ and the length 3

The remaining angle:

$= pi - ((5pi)/8) + pi/4) = (pi)/8$

I am assuming that length AB (3) is opposite the smallest angle.

Using the ASA

Area $=(c^2*sin(A)*sin(B))/(2*sin(C))$

Area $=( 3^2*sin((5pi)/8)*sin((pi)/4))/(2*sin(pi/8))$

Area $=7.682$

A triangle has two corners with angles of pi / 4 pi / 4 and (5 pi )/ 8 (5 pi )/ 8 . If one side of the triangle has a length of 3 3 , what is the largest possible area of the triangle?