Follow the steps below:
1. from triangle ABD find AB & AD using cosine rule.
2. find AC from given equation
3.find CD from right triangle ACD
4.find BC from triangle BCD
Now you has all three sides of triangle ABC, and can find m<BAC.
I followed thru from post5 to get a corrected solution.Here are my answers. I increased the figure 10 times to avoid fractions less than 1
AD = 9.54 AC= 7.78 DC= 3.48 Angle DAC = 20 degrees Angle BAC =80 degrees Angle ACD = 110 degrees