A triangle has sides A, B, and C. The angle between sides A and B is (2pi)/32π3. If side C has a length of 2 2 and the angle between sides B and C is pi/12π12, what is the length of side A?

1 Answer
Barney V.
Dec 8, 2016

0.250.25

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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