A triangle has sides A, B, and C. The angle between sides A and B is #(5pi)/6#. If side C has a length of #36 # and the angle between sides B and C is #pi/12#, what are the lengths of sides A and B?

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Answer 1 · 2016-03-10T13:05:25

#=> A = B ~~ 18.635 # to 3 decimal places

A Diagram always helps!

Tony B

Known: The sum of the internal angles is #pi# radians (#180^o)#

Thus the angle between A and C is #pi-pi/12-(5pi)/6 = pi/12#

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#color(blue)("Using the sine rule")#

#C/(sin(/_AB)) =B/(sin(/_AC))=A/(sin(/_BC))#

Also as #/_AC = /_BC# then length #A=B#

#C/(sin(/_AB)) = 36/(sin((5pi)/6))= A/(sin( pi/12))#

#=>A = (sin(pi/12))/(sin((5pi)/6))xx36#

#=> A = B ~~ 18.635 # to 3 decimal places