Hi razemsoft 21,
AD = 10 sin 70/sin 100 =9.54
AC = rad3 - 9.54 = 7.78
cos 50 = AD^2 + DC^2 -AC^2/ 2*AD*DC DC only unknown
quadratic equation gives two solutions 3,47 is shortest which produces an oblique angle at ACD
cos DAC = AD^2 +AC^2 -DC^2/2*AD*AC = 20
ACD =110 BAC= 80
The sine law could have been used directly to give a value for ACD 0f 70 but since the question wanted an oblique angle the answer would be its supplement.See ambiguous case sin law