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Section 9.5Navigation & Surveying
Pre-Calculus
Learning TargetsSolve a Navigation and Surveying
application problem by using law of sines, law of cosines, or the area of a triangle.◦Identify what compass bearing and
compass reading means◦Construct a picture from the word
problem◦Identify which method to use◦Solve
Navigation: Compass BEARINGThe course of a ship or plane is
the angle measured clockwise starting at the north direction.
Example 1Practice Constructing Pictures1. Draw the picture of a plane on a
course of 190°
2. Draw the picture of a boat on a course of 60°
3. Draw the picture of a boat that started on a course of 330° then after some time changed to a course of 200°
Surveying: Compass READINGIn surveying, a compass reading
is given an acute angle from the north-south line to the east or west.
Example 2Practice Constructing Pictures1. Draw the picture. Start at a granite
post and proceed 5ft west. Then travel along a bearing of S45°E for 7ft.
2. Draw the picture. Start at a tree and proceed along a bearing of N60°E for 4ft, then along a bearing of S40°E for 7ft, and finally along a bearing of S30°W for 2 ft. Then go back to the tree in a straight line.
Example 3: Word Problem (pg 359)A ship proceeds on a course of 300° for 2
hours at a speed of 15 knots (1 knot = 1 nautical mile per hour). Then, it changes course to 230°, continuing at 15 knots for 3 more hours. At that time, how far is the ship from its starting point?
62 Nautical Miles
Example 4: Word Problem (pg 360)From a granite post, proceed 195ft east
along, then along a bearing of S32°E for 260ft, then along a bearing of S68°W for 385ft and finally along a line back to the granite post. Find the area of the plot of land
84,800 ft2
Example 5: Word ProblemA plane proceeds on a course of 310o for 2
hours at 150 mph. It then changes direction to 200o continuing for 3 more hours at 160 mph. At this time, how far is the plane from its starting point?
471 Miles
Example 6:A post is driven in a certain spot. Proceed
due east for 300 ft, then proceed S 40o E for another 150 feet. Turn direction again S 60o W for 400 feet and then back to the post in a straight line. Find the area.
76853 sq ft.
HomeworkTextbook Pg 362 #11, 13, 15, 16
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