sec 9.5 applications of trigonometry to navigation and surveying
TRANSCRIPT
Which direction?
• Navigation… used by ships, planes etc.
Start on the y-axis.ClockwiseGiven using 3 digits
9.5 Applications of Trigonometry to Navigation and Surveying
Objective
.To use trigonometry to solve navigation and surveying problems
The course of a ship or plane is the , measured clockwise,
from the north direction to the direction of the ship or plane.
9.5 Applications of Trigonometry to Navigation and Surveying
Objective
.To use trigonometry to solve navigation and surveying problems
The course of a ship or plane is the , measured clockwise,
from the north direction to the direction of the ship or plane.
Objective
.To use trigonometry to solve navigation and surveying problems
The course of a ship or plane is the , measured clockwise,
from the north direction to the direction of the ship or plane.
Bearing of from 240A B Bearing of from 060B A
Example 1. A ship proceeds on a course of 300º for 2 hours at a speed of 15 knots (1 knot = 1 nautical mile per hour). Then it changes course to 230º, continuing at 15 knots for 3 more hours. At that time, how far is the ship from its starting point?
N
30
N
45
x
606050
Law of
Cosines
2 2 2
1 2 1 22 cosOPP ADJ ADJ ADJ ADJ
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
the starting point?
N
30
N
45
x
606050
Law of
Cosines
2 2 2
1 2 1 22 cosOPP ADJ ADJ ADJ ADJ
2 2 230 45 2 30 45 cos110
62.0 nautical miles
x
x
Which direction?• In surveying, a compass reading is usually
given as an acute angle from the north-south line toward the east or west line.
a) Start on the y-axis.
b) Clockwisec) The angle is
always acute.
In surveying, a compass reading
is usually given as an acute
from the north-south line toward
the east or west.
NE Sandy and NE 40th meet at approx 58 degree angle.
Give directions from the Formation Area to the disband Area.a) Using
navigation system.
b) Using the survey method.
Basic Hints and rules• Make a diagram… give yourself drawing
space all around the diagram.• Although drawing to scale might be hard,
come as close to a scale as possible.• Write all the given information on your
diagram.
Basic Hints and rules• Include a lightly drawn x and y axes at each
point.• Find as many angles and sides as you can.• Apply as many geometry rules as you can.
Camping:
Give direction from the camp site to each of 4 points of interest:
a) The river
b) The lake
c) To the tower
d) The hill
Generate clarifying
questions!
Example 2. Very often a plot of land is taxed according to 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 S32ºE for 260 ft, then along a bearing of S68ºW for 385 ft, and finally along a line back to the granite post.
With these types of problems, a careful diagram is essential. Next slide will demonstrate all the steps.Make sure to have your geometric tools and math wits about you!
GTakser Hill Road
195 ft Q
32º260 ft
R68º
385 ft
S
90°90°
32°
80°
area of ∆ GQS=35,561.49area of ∆ GRS=49,289.63
TOTAL: 84,851.12
A plot of land is taxed according to its area. Sketch the plot
of land described, then find its area.
o
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.
195 ftN
260 ft32
N
68
385 ft
2
2 2 2
1195 260 sin122 21,500 ft
2
195 260 2 195 260 cos122
399 ft
K
x
x
399 ft
2
2
sin sin122
195 399
24.5 55.5
1399 385 sin 55.5 63,300
84,
ft
8
2
0 ft 0
K
Total Area
x 24.5
55.5
90
1sin
2k ab C
500 m NE; 300 m E; 200 m S15 ; BackE
15. N
500 m
300 m
200 m
15
401d
2 2 2300 200 2 300 200 cos105
401 m
d
d
1
2
1300 200 sin105
2
29,000 m
K
K
N
N45
sin sin105
200 401
28.8
135 28.8 106.2m
2
2
1500 401 sin106.2
2
96,000 m
K
K
2125,000 mArea
90
Presentation
45
16.
260 m
182d
2 2 2240 280 2 240 280 cos 40
182 m
d
d
2
1240 280 sin 40
2
21,600 m
K
K
N
2
1260 182 sin 53
2
18,900 m
K
K
240,500 mArea
240 m40
280 m
sin sin 40
240 182
58.0
53
5882
Presentation260 m SW; 240 m S; 280 m N40 E; Back
oProceed S78 W for 250 m.
Then S15 E for 180 m.
Then N78 E.
Then N30 E to the
starting point.
N
250 m78
N
15
180 m
N78
1d
N
2d30
78
871K
30
48
3d
2 2 23
3
180 250 2 180 250 cos87
300.32 m
d
d
sin sin87
180 300.32
36.8
11.2
132
36.8
1
1
300.32
sin11.2 sin13278.49 m
d
d
2K
21 2 29,500 mK K
Presentation
Homework:
• Sec 9.5 written exercises
• 7-13 odds; 15, 16, 17
In class Exit Slip:• Page 353 Problem
#17.• Only full solutions
will be considered.
If you were absent, see Navi for make up Exit Slip.
Applications of Trig to Navigation and SurveyingThe course of a ship or plane is the angle, measured clockwise, from the north direction to the direction of the ship or plane.
As shown, the compass bearing of one location from another is measured in the same way. Note that compass bearings and courses are given with three digits, such as 060º rather than 60º
Example 1. A ship proceeds on a course of 300º for 2 hours at a speed of 15 knots (1 knot = 1 nautical mile per hour). Then it changes course to 230º, continuing at 15 knots for 3 more hours. At that time, how far is the ship from its starting point?
5060
60
Example 1. A ship proceeds on a course of 300º for 2 hours at a speed of 15 knots (1 knot = 1 nautical mile per hour). Then it changes course to 230º, continuing at 15 knots for 3 more hours. At that time, how far is the ship from its starting point?
5060
60
Example 2. Very often a plot of land is taxed according to 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 S32ºE for 260 ft, then along a bearing of S68ºW for 385 ft, and finally along a line back to the granite post.
399
24.5
55.5
Example 2. Very often a plot of land is taxed according to 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 S32ºE for 260 ft, then along a bearing of S68ºW for 385 ft, and finally along a line back to the granite post.
399
24.5
55.5