Solution: Take PA as one side, make a regular triangle APQ outward, and then connect it with BQ, and you will know.

PQ=PA=3，∠APQ=60，

Because AB=AC, PA=QA, ∠ CAP+∠ PAB = 60 = ∠ PAB+∠ BAQ, that is ∠CAP=∠BAQ, so

△CAP?△BAQ

Available: CP=BQ=5,

At △BPQ, PQ=3, PB=4, BQ=5. From Pythagorean Theorem, it can be known that △BPQ is a right triangle. therefore

∠BPQ=90

therefore

∠APB=∠APQ+∠BPQ=60 +90 = 150 .