sin(A+B) = 8/15 +[sqrt(5) /5] ------------positive sine value

So, (A+B) is in the 1st or 2nd quadrants.

cos(A+B) = 4sqrt(5) /15 -[2/5]

= 4sqr(5) /15 -[6/15] --------------------positive cosine value

So, (A+B) is in 1st or 4th quadrants.

Hence, (A+B) is definitely in the 1st quadrant.

Therefore, (A+B) is an acute angle.