8/4/2019 11.Shortest Distance Between Two Points

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Mathematics Form 5

ACTIVITY SHEET

Pupils Copy

Lesson 99: Longitude of a point on a parallel of latitude

1

Find the shortest distance betweenXand Yfor the diagrams given below:

N

S

O

70N

0

X

Y

10S

180W

N

S

OY

35SX

20E

160W

Question 1

Question 2

Question 3

Question 4

N

S

O

40E

50NX Y

140W

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Mathematics Form 5

2

i) Find the shortest distance from CityA(45N, 120W) to CityB(35N, 60E).

ii) Find the shortest distance from AirportP(27S, 30E) to Airport Q(70N, 150W).

iii) The shortest distance from T(80N, 80W) to U(xN, 100E) is 3600 n.m.

Find the value ofx.

8/4/2019 11.Shortest Distance Between Two Points

3/4

Mathematics Form 5

ACTIVITY SHEET

Teachers Copy

Lesson 99: Longitude of a point on a parallel of latitude

1

Find the shortest distance betweenXand Yfor the diagrams given below:

N

S

O

70N

0

X

Y

10S

180W

N

S

OY

35SX

20E

160W

The shortest distance ofXand Yis along the greatcircle passing through the North Pole.

Longitude difference = 40+ 140

= 180

XOY= 1805050

= 80

= 80 60

= 4800

Answer: 4800 nautical miles

Answer: 7200 nautical miles

Answer: 6600 nautical miles

Question 1

Question 2

Question 3

Question 4

The shortest distance ofXand Yis along the greatcircle passing through the North Pole.

Longitude difference = 0+ 180

= 180

XOY= 10+ 90+ 20= 120

= 120 60

= 7200

The shortest distance ofXand Yis along the great

circle passing through the South Pole.

Longitude difference = 20+ 160

= 180

XOY= 1803535

= 110

= 110 60

= 6600

N

S

O

40E

50NX Y

140W

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Mathematics Form 5

2

i) Find the shortest distance from CityA(45N, 120W) to CityB(35N, 60E).

Answer: 6000 nautical miles

ii) Find the shortest distance from AirportP(27S, 30E) to Airport Q(70N, 150W).

Answer: 8220 nautical miles

iii) The shortest distance from T(80N, 80W) to U(xN, 100E) is 3600 n.m.

Find the value ofx.

Answer:x = 40

The shortest distance ofAandB is along the greatcircle passing through the North Pole.

Longitude difference = 20+ 160

= 180

AOB = 1804535

= 100

= 100 60

= 6000120W

N

S

O

45

AB

60E

35

The shortest distance ofPand Q is along the greatcircle passing through the North Pole.

Longitude difference = 30+ 150

= 180

POQ = 20+ 90+ 27

= 137

= 137 60

= 8220S

O

70

Q

P

30E

27

150W

The shortest distance ofTand Uis along the greatcircle passing through the North Pole.

Longitude difference = 80+ 100

= 180

TOU=

= 60so, NOU= 6010

= 50

Thusx = 90 50

= 40

80W

S

O

80

T

U

100E

x