1. Warm Up
1.) A triangle has the following sides/angle. How many triangles can be formed? <C = 25˚ b = 3 c = 2 2.) A triangle has the following sides/angle. How many triangles can be formed? <B = 40˚ a = 12 b = 6

2. Section 9.5 Navigation & Surveying
Pre-Calculus

3. Learning Targets
Solve 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

4. Navigation: Compass BEARING
The course of a ship or plane is the angle measured clockwise starting at the north direction.

5. Example 1 Practice Constructing Pictures
1. 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°

6. 9.5 Applications of Trig to Navigation and Surveying
A plane proceeds on a course of 310° for 2 hours at 150 mph.  It then changes direction to 200° continuing for 3 more hours at 160 mph.  At this time, how far is the plane from its starting point?
471 Miles

7. Surveying: Compass READING
In surveying, a compass reading is given an acute angle from the north-south line to the east or west.

8. Example 2 Practice Constructing Pictures
1. 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.

9. 9.5 Applications of Trig to Navigation and Surveying
Posts are used to outline a plot of land. From the first post, proceed due east for 300 ft, then proceed S 40° E for another 150 feet.  Turn direction again S 60° W for 400 feet and then back to the first post in a straight line.  Find the area.
76853 sq ft.

10. 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

11. 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

12. Homework
Textbook Pg 362 #11, 13, 15, 16