Answer:
379,442 AU
Explanation:
The angle bisector is the altitude of the triangle. The resulting right triangle has a distance of 1 AU opposite the 0.000151° angle. The length we're interested in is the hypotenuse of the triangle. The relevant trig relation is ...
Sin = Opposite/Hypotenuse
Hypotenuse = Opposite/Sin
E-S distance = (1 AU)/sin(0.000151°) ≈ 379,442 AU
The star is about 379,442 AU from Earth.