An aircraft is flying at a constant altitude with velocity magnitude r₁ (relative to the air) and angle θ₁ (in a two-dimensional coordinate system). The magnitude and direction of the wind are r₂ and θ₂, respectively. Suppose that the wind angle is uniformly distributed between 10 and 20 degrees and all other parameters are constant. Determine the probability density function of the magnitude of the resultant vector r = [r₁² + r²₂ + r₁ r₂ (cosθ₁ – cosθ₂)]^0.5.