A commuter airplane starts from an airport and takes the route shown in the figure below. The plane first flies to city A, located 175 km away in a direction 30.0° north of east. Next, it flies for 150 km 20.0° west of north, to city B. Finally, the plane flies 190 km due west, to city C. Find the location of city C relative to the location of the starting point.
distance km
angle ° west of north

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  1. Do a vector addition. If you don't know how, you need to study harder.

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  2. airport to A
    Distance east: cos 30 = east / 175

    east = 151.55 km

    Distance north: sin 30 = north / 175 = 87.5 km

    A to B

    Distance north: cos 20 = north / 150

    north = 140.95 km

    Distance west: sin 20 = west / 150 = 51.3km

    B to C =190km west

    Distance west from airport to C=-151.55 + 51.3 + 190 = 89.75km

    Distance north from airport = 87.5 + 140.95 = 228.45

    Using Pythagoras theorem

    h^2 = 89.75 ^ 2 + 228.95 ^ 2

    h = 245.45 km

    tan theta = 89.75/228.45

    theta = 21.45 deg

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  3. Show all necessary steps

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