A small plane leaves Victoria airport and flies at a compass heading of 330°. If the plane cruises at 125km/he for 90mins, how far north and how far west will the plane gave flown

Using the standard "compass heading"

http://www.allstar.fiu.edu/aero/fltmidcomp.htm

that would be 120° based on standard trig notation.

what If I told you the plane ends up at
(125(1.5)cos120°, 125(1.5)sin125°) ??

I don't understand how you got 125 and 120°

330 clockwise from North is 360 - 30 = 30 degrees west of north

That is 90+30 = 120 in math talk counterclockwise from the x axis.
However being a navigator and not a mathematician I will stick with 30 degrees west of north:)
How far did it go?
125 *1.5 hours = 187.5 km
west = 187.5 sin 30 = 93.75 km
north = 187.5 cos 30 = 162.4 km

Thank you

To determine how far north and how far west the plane has flown, we need to break down the velocity vector into its northward and westward components.

Given:
Compass heading: 330°
Cruising speed: 125 km/h
Time: 90 minutes

Step 1: Convert the compass heading to a standard mathematical angle.
To do this, subtract 90° from the compass heading since standard mathematical angles start from the positive x-axis (east). In this case, 330° - 90° = 240°.

Step 2: Convert the cruising speed from km/h to km/min.
The plane is cruising for 90 minutes, so we need to convert the cruising speed from kilometers per hour to kilometers per minute. Since there are 60 minutes in an hour, we divide 125 km/h by 60 to get the speed in kilometers per minute: 125 km/h ÷ 60 = 2.08 km/min.

Step 3: Calculate the northward and westward components of the velocity vector.
We can use trigonometry to calculate the northward (y) and westward (x) components. The northward component is given by the formula:
northward component = cruising speed × sin(angle)

Similarly, the westward component is given by the formula:
westward component = cruising speed × cos(angle)

In this case, the angle is 240° and the cruising speed is 2.08 km/min. Plugging these values into the formulas, we have:
northward component = 2.08 km/min × sin(240°)
westward component = 2.08 km/min × cos(240°)

Step 4: Calculate the distance flown north and west.
To find the distance flown north, we multiply the northward component by the time:
distance flown north = northward component × time

Similarly, to find the distance flown west, we multiply the westward component by the time:
distance flown west = westward component × time

In this case, the time is 90 minutes. Plugging in the values and calculating the distances:
distance flown north = (2.08 km/min × sin(240°)) × 90 min
distance flown west = (2.08 km/min × cos(240°)) × 90 min

Calculating these distances will give you the specific values for how far north and how far west the plane will have flown.