If sinθ·cosθ = 1/3 and θ is acute, then sinθ + cosθ equals:

$(sin\theta +cos\theta {)}^2=1+2$sinθ·cosθ = 1 + 2/3 = 5/3, and the sum is positive for an acute angle, so sinθ + cosθ = √(5/3) = √15/3 ≈ 1.291. Forgetting the square root leaves 5/3, and misreading √(5/3) as √5/3 ≈ 0.745 gives a value smaller than 1, which is impossible here.