A triangle has sides A, B, and C. The angle between sides A and B is $(2pi)/3$ . If side C has a length of $1$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2018-07-14T10:10:47

$a=sqrt(6)/3$

At first we compute the third angle:
$pi-pi/12-2/3*pi=(12pi-pi-8pi)/12=3/12pi=pi/4$
So we get by the Theorem of sines:

$a=sin(pi/4)/sin(2/3pi)$
Not that

$sin(pi/4)=sqrt(2)/2$
$sin(2/3*pi)=sqrt(3)/2$

so we get

$a=(sqrt(2)/2)/(sqrt(3)/2)=sqrt(2)/sqrt(3)=(sqrt(2)*sqrt(3))/(sqrt(3)*sqrt(3))=sqrt(6)/3$

A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/3(2pi)/3. If side C has a length of 1 1 and the angle between sides B and C is pi/12pi/12, what is the length of side A?