x^2/5-y^2/3= 1

a^2=5,b^2=3，

c^2=a^2+b^2=8,c=2√2

|F 1F2|=2c=4√2

The area of triangle f1af 2 =1/2 * | f1f 2 | * the ordinate of a point.

Therefore, the ordinate of point A is =2*2√2/|F 1F2|= 1.

The abscissa of point A = √ (15+5)/3 = √ 2+05/3.

Then find |AF 1| and |AF2|.

Then the angle F 1AF2 is calculated by cosine theorem.