Is my diagram correct An airplane flies 200 km due west from city A to city B an

Question

Is my diagram correct

An airplane flies 200 km due west from city A to city B and then 280 km in the direction of 28.5° north of west from city B to city C. (a) In straight-line distance, how far is city C from city A? Use Pythagorean theorem to solve d2 446.072 133.612 d2-198,978.45 km17,851.63 km d2-216,830.08 km d square root (216,830.08 km) d 466 km (larger image next slide) City C -200 km 0 AB opposite to angle sin points up-positive -280 cos 28.5°280 sin 28.5 BC . = 280 sin 28.5 28.5 246.07 133.61 133.61 City B 200 km City A Total 133.61 -446.07 adjacent to angle = cos points to the left- points to left -200 knm -280 km cos 28.5 Why did -446.07 change to +446.07? Do you take absolute value? 246.07 tan = 133.61 446.07 Now find the angle Is my diagram correct = tan-1 133.61 446.07 x is adjacent to the angle y is opposite the angle. Use tan to find the angle = 16.70 N of w

Explanation / Answer

Yes. When one applies Pythagorean theorem, one takes into account only the distances(in magnitude, neglecting the sign i.e. the direction), as they represent the sides of a right angle triangle.

Whereas, the negative signs appearing in the components of the vector indicate the direction. Here, negative sign indicates negative X axis ( i.e. towards West )

The diagram is perfectly correct.

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