A triangle has two corners with angles of $\frac{π}{4}$ $pi / 4$ and $\frac{5 π}{8}$ $(5 pi )/ 8$ . If one side of the triangle has a length of $12$ $12$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-20T11:44:22

Largest possible area of $Delta = 122.9117$

Given are the two angles $(5pi)/8$ and $pi/4$ and the length 12

The remaining angle:

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

I am assuming that length AB (12) is opposite the smallest angle.

Using the ASA

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

Area $=( 12^2*sin((5pi)/8)*sin((pi)/4))/(2*sin(pi/8))$

Area $=122.9117$

A triangle has two corners with angles of pi / 4 π4 pi / 4 and (5 pi )/ 8 5π8 (5 pi )/ 8 . If one side of the triangle has a length of 12 1212 , what is the largest possible area of the triangle?