an airplane is headed north with a constant velocity of 450km/h. the plane encounters a wind from the west at 100 km/h.
a) in 3h, how far will the plane travel?
b) in what direction will the plane travel?
I should point out that there I made a mistake, that is the angle the plane makes with the horizontal so the actual angle is $\displaystyle 90 - \arctan(4.5)$.
When I drew my diagram I put the plane at the origin and drew a horizontal line right to represent the wind (100) and a vertical line up to represent the plane going north (450)
I then made a right-angled triangle from these lines with an angle \theta between them. Part a is asking for the hypotenuse which is Pythagoras' as you got.
Part b is one of the trig ratios, since the opposite and the adjacent are known directly I used $\displaystyle tan \theta = \frac{\text{Opposite}}{\text{Adjacent}} = \frac{450}{100} = 4.5$.
However, this is the angle is makes with East (as I forgot in my last post), to find the answer from North we need to take this angle from 90.
$\displaystyle 90 - \arctan (4.5) = 12.5$