To find: The distance of the boat from the harbor.
The distance of the boat from the harbor is approximately 53 nautical miles.
Given information:
Given, a boat leaves harbor and travels at 20 knots on a bearing of 90°. After 2 hr, it changes course to a bearing of 150° and continues at the same speed for another hour. The entire trip is of 3-hr.
Calculation:
The figure representing the data is:
Let the boat start at point A . The boat travels on a bearing of 90° and at 20 knots for 2 hours to reach point B . Here the boat changes the course to a bearing of 150° and travels for 1 hour. Since the boat travels at a speed of 20 knots, the distance travelled in 2 hours is 40 nautical miles and in 1 hour is 20 nautical miles. Extending the line AB to make a perpendicular to point C . Let,
From the figure of the triangle BCD,
Using the trigonometric function definitions,
From the triangle ADC:
The distance of the boat from the harbor is approximately 53 nautical miles.
Conclusion:
The distance of the boat from the harbor is approximately 53 nautical miles.
Chapter 4 Solutions
PRECALCULUS:GRAPHICAL,...-NASTA ED.
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