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

1 Answer
May 19, 2016

2 sqrt(6) (sqrt(3)-1)

Explanation:

Assuming angles opposite to sides A, B and C are /_A, /_B and /_C, respectively.

Then
/_C = pi/3 and /_A = pi/12

Using Sine Rule

(Sin/_A)/A = (Sin/_B)/B = (Sin/_C)/C

we have,
(Sin/_A)/A = (Sin/_C)/C
(Sin(pi/12))/A = (Sin(pi/3))/12
A=(sqrt(3)-1)/(2 sqrt(2))*12*1/(sqrt3/2)
or, A=2 sqrt(6) (sqrt(3)-1)
or, A~~3.586