What is the resultant velocity for a plane that is flying due east at 33m/s that is also being carried due north at 12m/s by the wind

  v = 35.11 m / s,    θ = 20º    north of east

Explanation:

This is a compound problem of relative velocities, we can use the Pythagorean theorem to find the modulus of the resulting velocity

            v² = v₁² + v₂²

where the eastward velocity is v₁=33 m/s and the northward velocity

v₂=12 m / s

            v =

             v = 35.11 m / s

the direction of this velocity can be found with the uses of trigonometry

           tan θ = v₂ / v₁

           θ = tan⁻¹ v₂ / v₁

           θ = tan⁻¹ 12/33

           θ = 20º

this angles is north of east

the working equation for the angular size is the product of the physical size and 360 degrees divided by the product of two pi and distance from earth. the minimum size would be 0.559 degrees while the maximum size would be 0.49 degrees. 

3. dark matter

empty space could also be a simple vacuum