A triangle has two corners with angles of $\frac{3 π}{4}$ $(3 pi ) / 4$ and $\frac{π}{6}$ $( pi )/ 6$ . If one side of the triangle has a length of $4$ $4$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-20T11:39:46

Largest possible area of the triangle $Delta = 10.9282$

Given are the two angles $(3pi)/4$ and $pi/6$ and the length 4

The remaining angle:

$= pi - (((3pi)/4) + pi/6) = (pi)/12$

I am assuming that length AB (4) is opposite the smallest angle.

Using the ASA

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

Area $=( 4^2*sin((3pi)/4)*sin((pi)/6))/(2*sin(pi/12))$

Area $=10.9282$

A triangle has two corners with angles of (3 pi ) / 4 3π4 (3 pi ) / 4 and ( pi )/ 6 π6 ( pi )/ 6 . If one side of the triangle has a length of 4 44 , what is the largest possible area of the triangle?