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

1 Answer
Barney V.
Dec 8, 2016

#0.25#

Explanation:

#pi/12=0.261799387°=0°15'48''#
#2pi/3=2.094395102=2°5'40''#
Cosine rule:-
#a^2=b^2+c^2-2*b*c*CosA#
#b^2=a^2+c^2-2*a*c*CosB#
#c^2=a^2+b^2-2*a*b*CosC#
#(BC)=2*sin0261799387/sin2.094395102#
#=0.00913849/0.03654595#
#BC(a)= 0.25#
BC=side a,AC=side b,AB = side c
pi/12=.261799387° (0°15'42.18'')
2pi/3=2.094395102° (2°5'40'')
180°-(0°15'42.48'+2°5'40'')=177°38'37''
#(AC)/(sin177°38'37'')= (BA)/(sin2°5'40'')#

#AC=(2*Sin177°38'37'')/(Sin2°5'40'')#
#AC=0.0822/0.0365#
#AC(b)=2.25#
#c^2=(25)^2+(2.25)^2-2(0.25)(2.25)*0999331942#
#=0.0625+50625-1.124#
#AB(c)=2.0(given)

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