Maths Quest A Year 11 for Queensland
WorkSHEET 6.2
Chapter 6 Earth geometry
Earth geometry
WorkSHEET 6.2
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Name: ___________________________
Use the world map above for the following questions, where necessary.
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State whether the following pairs of points lie
on the same line of longitude or the same line
of latitude.
(a) X (20ºN, 50ºE) and Y (20ºN, 50ºW)
(a) latitude
(b)
P (50ºN, 50ºW) and Q (20ºN, 50ºW)
(c) latitude
(c)
R (0º, 20ºE) and T (0º, 20ºW)
(d) longitude
(d)
C (0º, 0º) and D (50ºS, 0º)
(b) longitude
Determine the angular distance between the
following pairs of points.
(a) A (23ºN, 0º) and B (50ºN, 0º)
(a) angular distance
= 50º – 23º
= 27º
(b)
F (50ºS, 23ºW) and G (20ºN, 23ºW)
(b) angular distance
= 50º + 20º
= 70º
(c)
J (70ºS, 50ºE) and K (70ºS, 40ºE)
(d)
X (0º, 20ºW) and Y (0º, 40ºE)
(c) angular distance
= 50º – 40º
= 10º
(d) angular distance
= 20º + 40º
= 60º
Maths Quest A Year 11 for Queensland
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Chapter 6 Earth geometry
On a great circle, 1º  111.2 km. Calculate the
distance in km between the following pairs of
locations.
(a) P (50ºS, 100ºE) and Q (12ºN, 100ºE)
(b)
A (40ºN, 20ºW) and B (75ºN, 20ºW)
(c)
C (0º, 40ºW) and D (0º, 20ºE)
WorkSHEET 6.2
(a) angular distance
distance in km
(b) angular distance
distance in km
(c) angular distance
distance in km
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On a small circle,
1  111.2 km. cos  km
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P (40ºS, 20ºW) and Q (40ºS, 30ºE)
When the angular distance between two
locations is greater than 180º, the shortest
distance between the two points is found by
subtracting the angle from 360º.
= 75º – 40º
= 35º
= 35  111.2 km
= 3892 km
= 40º + 20º
= 60º
= 60  111.2 km
= 6672 km
angular distance = 20º + 30º
= 50º
distance in km = 50  111.2 km cos 40º
= 4259 km
(a)
These two points be on the same small
circle (30ºN).
Angular distance = 150º + 100º
= 250º
This is over 180º.
So, shortest angular distance
= 360º – 250º
= 110º
So, shortest distance between Y and Z
= 110  111.2 cos 30º
= 10 593 km
(b)
Points D and F lie on the same great
circle (the equator)
Angular distance = 110º + 120º
= 230º
This is over 180º.
So, shortest angular distance
= 360º – 230º
= 130º
So, shortest distance between D and F
= 130  111.2 km
= 14 456 km
Find the shortest distance between the
following pairs of points.
(a) Y (30ºN, 150ºE) and Z (30ºN, 100ºW)
(b)
= 50º + 12º
= 62º
= 62  111.2 km
= 6894.4 km
(a) angular distance = 77º – 50º
= 27º
distance in km = 27  111.2 km cos 25º
= 2721 km
where   parallel of latitude.
Calculate the distance in km between the
following pairs of locations (to the nearest km). (b)
(a) X (25ºN, 50ºE) and Y (25ºN, 77ºE)
(b)
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D (0º, 110ºW) and F (0º, 120ºE)
Maths Quest A Year 11 for Queensland
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Chapter 6 Earth geometry
The circumference of the equator represents an
angular distance of 360º. This distance also
represents a time period of 24 hours. Use this
information to determine the time period
equivalent to an angular distance of 1º of
longitude.
WorkSHEET 6.2
360   24 hours
24
1 
hour
360
1
1 
hour
15
1
1   60 min
15
1  4 min
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(a)
Longitude difference = 75º – 0º
= 75º
Time difference
= 75  4 min
= 300 min
= 5 hours
(b)
Longitude difference = 75º + 150º
= 225º
Time difference
= 225  4 min
= 900 min
= 15 hours
Time zones throughout the world are quoted
with reference to Greenwich Mean Time.
Explain each of the following.
(a)
Brisbane time is 10 hours ahead of
Greenwich Mean Time.
(a)
Brisbane is GMT + 10
(b)
(b)
New York is GMT – 5
New York time is 5 hours behind
Greenwich Mean Time.
Based on your answer for question 6, find the
time difference between the following pairs of
cities.
(a)
New York (40ºN, 75ºW)
and London (51ºN, 0ºW)
(b)
New York (40ºN, 75ºW)
and Sydney (34ºS, 150ºE)
Find the time difference between the following (a)
pairs of cities.
(a)
Los Angeles GMT – 8 and
Brisbane GMT + 10
(b)
Cape Town GMT + 1 and
Brisbane GMT + 10
(b)
Los Angles is 8 hours behind GMT and
Brisbane is 10 hours ahead of GMT.
 Time difference  10  (8)
 18 hours
Cape Town is 1 hour ahead of GMT and
Brisbane is 10 hours ahead of GMT.
 Time difference  10  (1)
 9 hours
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Maths Quest A Year 11 for Queensland
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Chapter 6 Earth geometry
Brisbane time is GMT +10. A plane leaves
Brisbane on a flight to London (GMT) at 8 a.m.
on Sunday. If the flight takes 20 hours, what
will be the local time in London when it
touches down?
WorkSHEET 6.2
Departure time  8 a.m. Sunday Brisbane time
Flight tim e  20 hours
 Arrival time  8 a.m.  20 hours (Brisbane time)
 4 a.m. Monday (Brisbane time)
Brisbane time is 10 hours ahead of London tim e
 Local time in London
 4 a.m. Monday  10 hours
 6 p.m. Sunday
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