Precalculus 2014
51

 PAGE: 490 SET: Exercises PROBLEM: 51

miles per hour at a bearing of .

miles per hour at a bearing of .

Draw a diagram to represent and using a scale of .

Observe the diagram :

The angle created by and - axis is .

Draw a horizontal where the tip of and the tail of meet, as shown in above figure.

makes a angle and makes a angle with the horizontal.

Thus, the angle created by and is .

Draw the resultant .

The three vectors form a triangle.

Use the law of cosines to find the magnitude of .

Law of cosines : .

Use the law of sines to find the angle opposite of .

Therefore, the angle opposite of is about .

To find the bearing of , subtract from .

Thus, the direction of is a bearing of .

Since the equilibrant vector is the opposite of resultant vector, it will have a magnitude of about at a bearing of about .

The magnitude of the quilibrant vector is about   at a bearing of about .

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