A triangle has sides A, B, and C. The angle between sides A and B is $(pi)/6$ . If side C has a length of $8$ and the angle between sides B and C is $(7pi)/12$ , what are the lengths of sides A and B?

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Answer 1 · 2018-06-01T11:54:41

$a=4*sqrt(2)*(1+sqrt(3))$ , $b=8sqrt(2)$

The third angle is given by $pi-9pi/12=pi/4$

By the Theorem of sines we get

$sin(pi/6)/sin(7*pi/12)=8/a$
so

$a=8*sin(7*pi/12)/sin(pi/6)$

and
$sin(pi/4)/sin(pi/6)=b/a$

so
b=8*sin(pi/4)/sin(pi/6)#

note that
$sin(7*pi/12)=1/4*sqrt(2)*(1+sqrt(3))$
$sin(pi/6)=1/2$
$sin(pi/4)=sqrt(2)/2$

A triangle has sides A, B, and C. The angle between sides A and B is (pi)/6(pi)/6. If side C has a length of 8 8 and the angle between sides B and C is (7pi)/12(7pi)/12, what are the lengths of sides A and B?