A triangle has two corners with angles of pi / 12 π12 and (5 pi )/ 8 5π8. If one side of the triangle has a length of 18 18, what is the largest possible area of the triangle?

1 Answer
sankarankalyanam
Dec 11, 2017

Largest possible area of the triangle is 458.776

Explanation:

Given are the two angles (5pi)/85π8 and pi/12π12 and the length 18

The remaining angle:

= pi - ((5pi)/8) + pi/12) = (7pi)/24=π−(5π8)+π12)=7π24

I am assuming that length AB (18) 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=( 18^2*sin((7pi)/24)*sin((5pi)/8))/(2*sin(pi/12))=182⋅sin(7π24)⋅sin(5π8)2⋅sin(π12)

Area=458.776=458.776

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