A triangle has sides A, B, and C. The angle between sides A and B is #pi/6#. If side C has a length of #3 # and the angle between sides B and C is #pi/12#, what is the length of side A?

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Answer 1 · 2017-10-14T16:50:06

#A=3/2(sqrt6-sqrt2)~=1.55#

The Euler theorem (or sine theorem) states that:

#A/sin hat(BC)=B/sin hat(AC)=C/sin hat(AB)#

Let's find A by using the relation:

#A/sin hat(BC)=C/sin hat(AB)#

from which:

#A=(C*sin hat(BC))/sin hat(AB)=(3*sin(pi/12))/sin (pi/6)#

#A=(3*1/4(sqrt6-sqrt2))/(1/2)=3/2(sqrt6-sqrt2)~=1.55#