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#