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 $32$ and the angle between sides B and C is $pi/12$ , what is the length of side A?

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Answer 1 · 2017-01-09T06:55:57

$A=16/3(3sqrt(2)-sqrt6)$

You would apply the Law of Sines:

$color(red)(A/sin hat(BC))=B/sin hat(AC)color(red)(=C/sin hat(AB))$

Then

$A/sin(pi/12)=32/sin((2pi)/3)$

and

$A=(32*sin(pi/12))/(sin((2pi)/3))=(cancel32^8*(sqrt(6)-sqrt(2))/cancel4)/(sqrt(3)/2)=16(sqrt(6)-sqrt(2))/sqrt(3)$

$=16*(sqrt(18)-sqrt(6))/3=16/3(3sqrt(2)-sqrt6)$

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 32 32 and the angle between sides B and C is pi/12pi/12, what is the length of side A?