Theory question 110
Latitude and Longitude(a) K (lat. 60°N, long, 50°W) is a point on the earth's surface. L is another point due east of K and the third point N is due south of K. The distance KL 3520 km and KN is 10951 km. Calculate (i) the longitude of L (ii) the latitude of N. (Take π = 22/7 and the radius of the earth = 6400 km)
(b) A man was allowed 20% of his income as tax free. He then paid 25 kobo in the naira on the remainder. If he paid N1,200.00 as tax, calculate his total income.
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(a)(i) Along latitude 60°: 3520 = θ/360 × 2 × 22/7 × 6400 cos 60°, so θ = 3520 × 360/20114 ≈ 63°.
Moving east 63° from 50°W: longitude of L = 63 − 50 = 13°E.
(ii) Along the meridian: 10951 = α/360 × 2 × 22/7 × 6400, so α ≈ 98°.
Moving south 98° from 60°N: 60 − 98 = −38, so N is at latitude 38°S.
(b) Taxable income = 80% of I; tax = 0.25 × 0.8I = 0.2I = 1200, so I = N6,000.
Crossing the Greenwich meridian or the equator switches W to E or N to S.