A triangle has two corners with angles of $pi / 12$ and $(7 pi )/ 8$ . If one side of the triangle has a length of $6$ , what is the largest possible area of the triangle?

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Answer 1 · 2017-12-05T12:27:00

Largest possible area of the triangle = 8.0031

Given are the two angles $(7pi)/8$ or $157.5^@$ and $pi/12$ or $15^@$ and the length 6

The remaining angle:

$180^@-(157.5^@+15^@)=17.5^@$

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 $=( 6^2*sin(17.5)*sin(157.5))/(2*sin(15))$

Area $=8.0031$

A triangle has two corners with angles of pi / 12 pi / 12 and (7 pi )/ 8 (7 pi )/ 8 . If one side of the triangle has a length of 6 6 , what is the largest possible area of the triangle?