1. 9.5 APPLICATION OF TRIG
NAVIGATION

2. The course of a plane or ship is measured clockwise from the north direction.
Notice that the courses are all three digit numbers.  The first has a course bearing of 110o, the second a course heading of 240o, and the third a course heading of 050o.

3. A plane proceeds on a course of 310o for 2 hours at 150 mph
A 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?
draw a diagram

4. The plane is 471 miles from its starting point.
The 50 on the right side of the picture comes from a complete circle minus the 310.  The 50 in the middle angle comes from alternate interior angles.
The 20 comes from the course heading of 200.  A straight line is 180 plus 20 more makes the bearing 200.
We can use law of cosines to find the missing side.  The included angle measures 70o. (Sum of the two angles)
x2 = (300)(480)Cos 70
x2 = Cos 70
x2 =
x = 471
The plane is 471 miles from its starting point.

5. 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 miles

6. Town T is 8 km northeast of village V
Town T is 8 km northeast of village V. City C is 4 km from T on a bearing of 150° from T. What is the bearing and distance of C from V?
≈ 7.96 km
Bearing of 74º

7. A plane flies 600 km on a course of 300°
A plane flies 600 km on a course of 300°. It then flies south for a while and finally flies on a course of 40° to return to its starting point. Find the total distance traveled.
≈ 2327 km

8. 9.5 APPLICATION OF TRIG
SURVEYING

9. In surveying, a compass reading is usually given as an acute angle measured from a north- south line toward the east or west. 

10. Northwest = N 45o W
Northeast = N 45o E
Southeast = S 45o E
Southwest = S 45o W

11. Sometimes a plot of land is taxed by its area. 
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.
draw a diagram

12. To find the area, we can divide the area into two triangles   One way to divide it is:

13. The other angle is found by 80 - 33.8 = 46.2o
We can calculate the top triangle's area right now!
K = (1/2)(300)(150)Sin 130
K = sq ft.
To find the other area, we need the length of the blue line and the degree of the bottom angle.
To find the length of the blue line, use law of cosines:
x2 = (300)(150)Cos 130
x2 =
x = 413
Now find the angle using the law of sines:
(Sin 130)/413 = (Sin y)/300
(300 Sin 130)/413 = Sin y
= Sin y
33.8o = y
The other angle is found by = 46.2o

14. Add the two areas together"
We can now find the area of the bottom triangle:
  K = (1/2)(413)(400)Sin 46.2
K = sq ft.
Add the two areas together"
= sq ft.

15. Sketch the plot of land described. Then find its area
Sketch the plot of land described. Then find its area. From a granite post, proceed 195 ft east along Tasker Hill Road, then along a bearing of S32°E for 260 ft, then along a bearing of S68°W for 385 ft, and finally along a line back to the granite post.
≈ 84,797 ft2

16. From the north corner of Park Avenue, a surveyor walked N38°E for 128 m and then S48°E. Find the surveyor’s distance and compass reading from his starting point.
≈ 190 miles due east

17. Assignment
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