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 #25 # and the angle between sides B and C is #pi/12#, what is the length of side A?
In general, the Law of Sine states that if a, b, and c are the lengths of the sides opposite angles
We only use the Law one pair of angles at a time. In this case, we know that the angle between A and B is
a = unknown
c = 25
Using the Law:
The value of
Solving the proportion:
NOTE: If we use the half-angle formula for sine instead of the difference formula, we obtain an answer that looks different but is equal to the above.