Question

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?

Answer 1

`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)