If we have two forces P and Q, resultant force is R and angle is θ

Then R² = P² + R² + 2PQ cos θ

Given, two vectors 2f and f√2 and the resultant force is f√10

=> (f√10)² = (2f)² + (f√2)² + 2 * 2f * f√2 cos θ

=> 10f² = 4f² + 2f² + 4√2f² * cos θ

=> 10f² = 6f² + 4√2f² * cos θ

=> 10 = 6 + 4√2 * cos θ

=> 10 - 6 = 4√2 * cos θ

=> 4 = 4√2 * cos θ

=> cos θ = 4/4√2

=> cos θ = 1/√2

=> cos θ = cos 45^°

=> θ = 45^° 

So, the angle is 45^°