Acute Angle Measure

Geometry Level 4

Triangle $ABC$ is an acute triangle. Let $E$ be the foot of the perpendicular from $B$ to $AC$ , let $F$ be the foot of the perpendicular from $C$ to $AB$ . If $2[AEF] = [ABC]$ , what is the measure (in degrees) of $\angle BAC$ ?

Details and assumptions

$[PQRS]$ denotes the area of figure $PQRS$ .