A triangle has sides A, B, and C. The angle between sides A and B is #(pi)/3#. If side C has a length of #18 # and the angle between sides B and C is #( pi)/8#, what are the lengths of sides A and B?

1 Answer
Alan P.
Oct 13, 2016

#abs(A)~~7.95#
#abs(B)~~20.61#

Explanation:

Given:
#color(white)("XXX")/_A:B = pi/3#
#color(white)("XXX")/_B:C=pi/8#
#color(white)("XXX")abs(C)=18#

#/_A:B=pi/3# and #/_B:C=pi/8color(white)("X")#
#color(white)("XXX")rarrcolor(white)("X")/_C:A = pi-(pi/3+pi/8) = (13pi)/24#

By the Law of Sines
#color(white)("XXX")abs(A)/sin(/_B:C) = abs(B)/sin(/_C:A)=abs(C)/sin(/_A:B)#

#abs(C)/sin(/_A:B) = 18/sin(pi/3) = 20.78461#

#abs(A)=20.78461 xx sin(/_B:C) = 20.78461 xx sin(pi/8) =7.953926#

#abs(B)=20.78461xxsin(/_C:A)=20.78461xxxin((13pi)/24) =20.60679#

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