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# LONGITUDE AND LATITUDE

CONTENT

1. Revision of Arc Length of a Curve
2. Calculation of Distance between Two Points on the Earth; Shortest Distance between Two Points (Great Cicle Routes)
3. Nautical Mile and Time Variations

## Revision of Arc Length of a Curve

Recall,

Arc length $$AB, L = \frac{θ}{360}×2πr$$   OR   Arc length $$AB, L = πr\frac{θ}{180}$$

but the angle $$θ$$ is given as, $$θ=\frac{180 L}{πr}$$  or  $$\frac{360 L}{2πr}$$

Perimeter of sector $$AB = \frac{θ}{360}×2πr + 2r$$

Area of sector $$AOB = \frac{θ}{360} ×πr^2$$

Examples:

1. In the figure below, AB is a chord of the circle centre O and radius 12cm, <AOB = 100⁰. Calculate correct to 3 s.f.

(a) The length of chord AB

(b) The length of arc ADB

(c) The perimeter of sector OADB

(d) The area of the shaded segment (Take $$π=\frac{22}{7}$$)

Solution:

(a) In the diagram, OM bisects <AOM and the chord AB.

Lesson tags: General Mathematics Lesson Notes, General Mathematics Objective Questions, SS3 General Mathematics, SS3 General Mathematics Evaluation Questions, SS3 General Mathematics Evaluation Questions First Term, SS3 General Mathematics First Term, SS3 General Mathematics Objective Questions, SS3 General Mathematics Objective Questions First Term
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