Using the Law of Cosines, let us determine angle BAC, first
So we have
28^2 = 50^2 + 50^2 - 2(2500)cos BAC
cos-1 [ (28^2 - 5000) / (-5000)] = BAC = about 32.52°
And since AC = AB then ACB = [180 - 32.52]/ 2 = about 73.74°
And ACD is supplemental to this = about 106.26°
And using the Law of Sines
sin ADC / 50 = sin 106.26 / 52 . so...using the sine inverse, we have
sin-1 (50sin106.26/ 52) = ADC = about 67.38°
So angle CAD = 180 - 106.26 - 67.38 = about 6.36°
Now...we can find CD with the Law of Sines, again
CD / sin 6.36 = 52 / sin 106.26
CD = 52 sin 6.36 / sin 106.26 = 6 units
