Theory question 113
Latitude and Longitude(a) Two places X and Y on the equator are on longitude 67°E and 123°E respectively. (i) What is the distance between them along the equator? (ii) How far is X from the North pole? [Take π = 22/7] and radius of the Earth as 6400 km).
(b) In the diagram, PQR is a circle centre O. N is the midpoint of chord PQ. |PQ| = 8 cm, |ON| = 3cm and ∠ONR = 20°. Calculate the size of ∠ORN to the nearest degree.
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(a)(i) Difference in longitude = 123 − 67 = 56°. Distance = 56/360 × 2 × 22/7 × 6400 ≈ 6258 km.
(ii) From the equator to the North Pole is 90° of a great circle: 90/360 × 2 × 22/7 × 6400 ≈ 10057 km.
(b) ON ⟂ PQ, so the radius OP = √(42 + 32) = 5 cm = OR.
In triangle ONR, sine rule: sin ∠ORN/3 = sin 20°/5, so sin ∠ORN = 0.2052 and ∠ORN ≈ 12°.
Both places are on the equator, so the equator itself is the circle to use.