For the triangle, you would use the tangent ratio to find 45 degrees (30 + 15) and then 30 for the measure of the opposite sides.
So, for triangle ABC,
tan (m<ABC) = Perpendicular/Base
So, tan 45 = AB/BC
tan 45 = AB/10
AB = 10 × 1 = 10
Now, for triangle DBC,
tan (m<BDC) = BD/BC
tan 30 = BD/10
BD = 10 * 0.577
BD = 5.77
This, AD = AB - BD = 10 - 5.77 = 4.23 ≈ 4.2 inches