Solution: If BC is the base, that is, AB=AC and if BC is waist BC=BA, ① point D is on the side of BC, ② if point D is on the extension line of CB, the answer can be obtained according to the properties of isosceles triangle and right triangle.

Solution: solution: ∵AD is the high line of BC side.

If BC is the bottom, that is, AB=AC, as shown in figure (1),

∴BD=DC,AD⊥BC,∠BAD=∠CAD

AD = BD

∴∠B=∠BAD=45

∴∠BAC=2∠BAD=90

If BC is waist BC=BA,

(1) If point D is on the side of BC, as shown in Figure (2),

And then in rt delta bad,

BA = 2AD，

∴∠B=30，

∴∠bac=75；

② If point D is on the extension line of CB, as shown in Figure (3),

Similarly, DBA = 30,

Then: ∠ ABC = 150,

∴∠BAC= 15。