OK, to find the length of side a for this problem, we're going to first of all need to find angle C, and then we're going to use law of sines so π - π force minus Pi 6, which if I change them all to common denominator twelfths, I get 7 Pi twelfths. So the law of sin says side a over sine of angle A, equal side C over sine of angle C. If I cross multiply, I get a equal 4 sine π force. We know sine π force is root 2 / 2 divided by sine of seven Pi twelfths. We do not know sine of seven Pi twelfths. So we're going to use an addition or subtraction formula. You could have also used your half angle formula here. So sine of three Pi twelfths plus four Pi twelfths does give me 7 Pi twelfths. That simplifies into π force plus π thirds. So expanding it, sine π force times cosine π thirds plus cosine π force times sine π thirds. Sine Π force is root 2 / 2, cosine π thirds is 1/2. Cosine π force is root 2 / 2. Sine Π thirds is root 3 / 2. Simplifying, and I'm going to pull out the root 2 / 2 because with the A equation I knew sine π force was root 2 / 2, so I want that part to cancel. So we get left root 2 / 2 times the quantity 1/2 plus root 3 / 2. Substituting it back into the a equation A equal four times the root 2 / 2 divided by root 2 / 2 times the quantity 1/2 plus root 3 / 2. Root 2 over twos are going to cancel. Getting a common denominator for the denominator part, making it a 11 fraction. We get one plus root 3 / 2. Invert and multiply. So we get 8 / 1 plus root 3. Can't leave a complex frac or can't leave the radical in the denominator, so we're going to multiply by the complex. Conjugate 1 minus root 3 on top and bottom. When we foil out the bottom, we get 1 -, 3 or -2. Negative 2 divides into the eight -4. When we distribute, we get a final answer of -4 + 4 root 3.