A commuter airplane starts from an airport and takes the route shown in the figu

Question

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

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 degree north of east. Next, it flies for 150 km 20.0 degree 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.

Explanation / Answer

assuming the straight line distance is what you have quoted.

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 pythagorus 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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