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