A triangle has two corners with angles of $\frac{π}{12}$ $pi / 12$ and $\frac{π}{6}$ $pi / 6$ . If one side of the triangle has a length of $6$ $6$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:36:41

Largest possible area of the $Delta = color (purple)(49.1769)$

Given are the two angles $(pi)/12$ and $pi/6$ and the length 6.

The remaining angle is $(pi - (pi/12 + pi/6) = (3pi)/4$

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

Area $=color (purple)(49.1769)$

A triangle has two corners with angles of pi / 12 π12 pi / 12 and pi / 6 π6 pi / 6 . If one side of the triangle has a length of 6 66 , what is the largest possible area of the triangle?