A triangle has two corners with angles of $(3 pi ) / 4$ and $( pi )/ 8$ . If one side of the triangle has a length of $7$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-08T10:01:21

Largest possible area = 17.3241

Given are the two angles $(3pi)/4$ and $pi/8$ and the length 7

The remaining angle:

$= pi - (((3pi)/4) + pi/8) = pi/8$

I am assuming that length AB (6) is opposite the smallest angle.

Using the ASA

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

Area $=( 7^2*sin(pi/8)*sin((3pi)/4))/(2*sin(pi/8))$

Area $=17.3241$

A triangle has two corners with angles of (3 pi ) / 4 (3 pi ) / 4 and ( pi )/ 8 ( pi )/ 8 . If one side of the triangle has a length of 7 7 , what is the largest possible area of the triangle?