A triangle has two corners with angles of pi / 6 π6 and (3 pi )/ 8 3π8. If one side of the triangle has a length of 12 12, what is the largest possible area of the triangle?

1 Answer
sankarankalyanam
Dec 11, 2017

Largest possible area of the triangle is 131.9005

Explanation:

Given are the two angles (3pi)/83π8 and pi/6π6 and the length 1

The remaining angle:

= pi - ((3pi)/8) + pi/6) = (11pi)/24=π−(3π8)+π6)=11π24

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))=c2⋅sin(A)⋅sin(B)2⋅sin(C)

Area=( 12^2*sin((11pi)/24)*sin((3pi)/8))/(2*sin(pi/6))=122⋅sin(11π24)⋅sin(3π8)2⋅sin(π6)

Area=131.9005=131.9005

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