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Chapter 4: Problem 39

A ship is 45 miles east and 30 miles south of port. The captain wants to sail directly to port. What bearing should be taken?

Short Answer

Expert verified
The bearing that should be taken is 124掳

Step by step solution

01

Draw and Label the Diagram

Firstly, sketch a right-angle triangle representing the ship's position with the port at the origin, the x-axis pointing east and the y-axis pointing south. The hypotenuse of the triangle will represent the path that the ship wants to take directly to port. Therefore, the ship is at the point (45,-30). Secondly, label the sides of the triangle. The eastward distance (45 miles) is the adjacent side and the southward distance (30 miles) is the opposite side.
02

Find the Angle Using Trigonometric Ratios

We can use tan 胃 = opposite / adjacent to calculate the angle from the east. Using the given opposite and adjacent sides: tan 胃 = -30/45 = -0.67. Use inverse tangent function to find angle 胃. Choosing the appropriate function on your calculator, we find that 胃 = arctan (-0.67), which gives a negative angle (about -34 degrees), because our axes are flipped, given we are measuring South of the East, not North as usual.
03

Convert Angle to Bearing

Finally, convert the negative angle from the last step to a bearing. Bearing is always a positive measurement clockwise from the North. Since our angle was measured from the East, subtract the 胃 found from 90掳 (since East is 90掳 from North) to get the bearing. So the bearing = 90掳 - (-34掳) = 124掳

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