Aplane is flying at 290km/h [e 42° s] relative to the air when the wind velocity is 65km/h [e 25° n]. calculate the velocity of the plane relative to the ground

320 km/h [E 31° S]

Explanation:

"E 42° S" means "east, 42° south", or 42° south from east.

"E 25° N" means "east, 25° north", or 25° north from east.

Taking east to be +x and north to be +y, the horizontal component of the velocity is:

vₓ = 290 cos (-42°) + 65 cos 25°

vₓ = 274 km/h

And the vertical component of the velocity is:

vᵧ = 290 sin (-42°) + 65 sin 25°

vᵧ = -167 km/h

The magnitude is found with Pythagorean theorem:

v² = vₓ² + vᵧ²

v² = (274)² + (-167)²

v = 320 km/h

And the direction is found with trig:

θ = atan(vᵧ / vₓ)

θ = atan(-167 / 274)

θ = -31°

Therefore, the plane's velocity relative to the ground is 320 km/h [E 31° S].

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. 

the total distance traveled by the car is

30km + 49km = 79 km .