(a)        A (60°N, 30°E) and B (60°N, 42°W) are two towns on the surface of the earth.  Calculate, correct to three significant figures, the:

1. radius of the circle of latitude on which A and B lie;
2. distance on the Earth’s surface between A and B along the circle of latitude.

 

[Take the radius of the Earth to be 6400 km and π = 3.142]

(b). In the diagram, O is the centre of the circle with radius 3.5 cm. 
If <BAC = 42°, calculate, correct to two decimal places, the area of the shaded segment.       [ Take p = 22  ].
                                                                                                                                                                                          7

observation

(a). This question on longitude and latitude was very popular among the candidates.  Many candidates exhibited a good understanding of longitude and latitude, latitudinal radius and using same to find the distance between the points on the earth’s surface, along the same latitude.  However, some candidates failed to correct their answer to three significant figures as required while others wrongly regarded the longitudinal difference as the degree of the latitude.

(b). The question on a composite body was a good test on mensuration. Many students, however, did not attempt the question even though it is not difficult. Those who attempted it did not get far before abandoning it or getting confused. Others used 42° instead of 84° to calculate the area of the sector which should not be so. They were expected to get <BOC = 84° (< at the centre is twice angle at the circumference of a circle).

Area of the sector will then be 84/360 x22/7 x 3.5² =

Area of ∆ BOC = ½ x 3.5 x 3.5 x sin 84 = 6.09 cm²

Hence, Area of segment = 8.98 cm² – 6.09 cm² = 2.89 cm²