Longitude and Latitude II SS3 Mathematics Lesson Note

The distance along a Great Circle  

Instructional Objectives: At the end of the lesson, students should be able to 

1. Locate places on the earth’s surface, 
2. Calculate the angular sum or difference of those places 
3. Apply the right formula 
4. Calculate the distance between the points along the great circle. 

Instructional Resource: Model of an Earth. 

Presentation: 

Step 1:  Identification of Prior Ideas: 

Mode: The whole class 

Teachers’ activities: the teacher asks the students from globe earth’s surface which is the great circle or small circle 

Students’ Activities: The great circles are lines of longitude and the equator while the small circles are parallels of latitudes. 

The teacher now explains that the distances along great circles are distances along the longitudes and equator. 

 Step 2:  Exploration:  

Mode: The whole class 

Teachers’ activities: The teacher leads the students to locate points and their angular difference or sum 

E.g   An aeroplane flies from a town P(40:N, 38:E) to another town Q(40:N, 22:W). it later flies to a third town T(28:N, 22:W). Calculate the angular difference or sum between:  

1. P and Q                 
2. Q and T 

Solution 

1. The angular difference b/w A and B;(WW) 
2. The angular difference b/w B and C;   

    E.g 3      Two places A and B lie on the same parallel of latitude 34.6:N. Their longitudes are 38.7:E and 22.3:W respectively. C is another point on the same meridian through A and its latitude is 35.4:S. Calculate correct to 3 s. f. the angular difference or sum between             

1. A and B            
2. A and C. 

Students’ Activities: Find the angular differences b/w B and C. Solution. 

  The angular sum b/w B and C; (NS)    Ѳ = 34.6: + 35.4: 

Ѳ = 70.0:  

Step 3: Discussion 

Mode:  The whole class 

Teachers’ activities: The teacher leads the students to Calculate the distance between the points along the great circle. 

In longitude and latitude, the earth is considered to be a sphere either of radius 6400 km or of a circumference   

  Where   is the angular difference 

R is the radius of the earth is 6400 km 

E.g 1. Two places on the same meridian have latitudes 23:S and 41:S. What is their distance apart measured along the meridian?    

 E.g. 2. Two places on the equator have longitudes 63:E and 132:E. How far apart are they measured along the equator? 

 Students’ Activities: Two places on the equator have longitudes 132:E and 126:W. 

Calculate their distance apart.                                                                                                                                           

  Step 4:Application 

Mode: The whole class 

Teachers’ Activities: The teacher leads the students to solve application problems 

E.g. 1 Calculate the distance between A (24:N, 30:E) and B (24:S, 30:E) measured along the great circle. Correct to 3 s. f. 

                                        E.g. 2 Two places on the same line of longitude are 3949 km apart. If one of them is at latitude 18:N and the other is in the southern hemisphere, what is the latitude of the other? 

   Students’ Activities:  The difference between two latitudes on the same side of the equator is 15:. Find the distance between two points lying on a longitude that cuts across the latitudes; if they lie at the points of intersection between the longitude and latitudes. 

Step 5: Evaluation:  

Mode: The whole class 

Teachers’ Activities: The teacher asks the students to solve 

The distance between two places on the same longitude is 5302 km. Find the difference between their latitudes. 

Students Activities: 

Assignment: 

Two points A (32:S, 30:E) and B (32:S, 12:W) are on the surface of the earth, P is another point on the same meridian as A and latitude 28:N. Calculate the shortest distance between A and P 

on the earth. Correct to 4 s. f. (Answer: 6700km) 

Reference Materials: 

• MAN Mathematics for SS 3 (3rd edition) 
• New General Mathematics for SS 3 by J. B. Channon et al 
• Multipurpose Mathematics for SSS by J. Olowofeso